Wild Goomy can only be found on Route 14, also known as Laverre Nature Trail. If you weren't able to encounter Goomy there, wild Sliggoo can be found on Route 19, the Grande Vallée Way.
Sliggoo will evolve into Goodra only under rain in the overworld, and triggering the weather condition via Rain Dance will not cause it to evolve. Rainy weather can be randomly triggered on Routes 8, 9, 10, 14, 15, 16, 18, 19, and 21, as well as Ambrette Town, Cyllage City, Geosenge Town, Shalour City, Laverre City, Couriway Town, and the Poké Ball Factory.
Introduced by the Pokédex as "the weakest Dragon-type Pokémon", Goomy actually becomes one of the strongest and most reliable ones after evolution, thanks to Goodra's fantastic special stats and decent physical bulk. Goodra is perhaps the most balanced of all pseudo-legendaries, in terms of offensive and defensive capabilities: unlike the dual Dragon/Flying-types, it lacks a glaring weakness to Ice and can actually tank super effective hits very well on the special side; while being monotype, it also benefits from the large movepool most pseudo-legendaries have and can make a good use of it in many situations, even more so in a generation where TMs are infinitely reusable. On top of that, it becomes available at a relatively early point in the game for such a powerful Pokémon, with the only downside being its rarity: since the Goomy encounter rate is low and it can be found only in one location, not many Kalos nuzlockers will get the option of adding one to their teams. Nevertheless, all who are graced with a Goomy as their first encounter will not be disappointed.
Gym #6 - Valerie (Laverre City, Fairy-type): Sliggoo has a good matchup against Mawile, which has no Fairy STAB; the Eviolite guarantees it to outdamage Mawile's Crunch by about twice with either Thunderbolt or Muddy Water. Both moves 2-3HKO the enemy. However, both Mr. Mime and Sylveon beat it with their Dazzling Gleam.
Celosia and Bryony (Poké Ball Factory, tag battle with rival): Sliggoo should enter this battlefield only if backed by Dragon Pulse and the Eviolite. Dragon Pulse 2HKOs Liepard, the major threat for Sliggoo; its Assurance is likely to hit for doubled damage, since Sliggoo is slow (though Manectric is also outsped by Liepard). Sliggoo can also get killed by residual damage after a turn of Liepard using Hone Claws and Assurance on the next, so it should be used in this battle only under safe conditions, and with a backup ready. If Sliggoo manages to take down Liepard, Manectric will then be 2-3HKOed easily.
Mable (Frost Cavern): Although Sliggoo's Muddy Water is a 2-3HKO against Houndoom, Houndoom's Foul Play also 3HKOs. Sliggoo can defeat Houndoom if it uses a different move in at least one of the first two turns, but should otherwise withdraw or be healed before proceeding.
Rival (Anistar City): Any Eviolite Sliggoo can wear down Meowstic, 3HKOing it with Dragon Pulse; it should preferably not fight Absol, however: its Swords Dance guarantees the Night Slash 2HKO, or OHKO with a critical hit (and Absol has Super Luck) after a single boost, and Dragon Pulse is not guaranteed to 2HKO in return. Vaporeon can be 3HKOed with Thunderbolt, and its Aurora Beam is only a 4HKO; Jolteon and Flareon are 3HKOed by Dragon Pulse and Muddy Water respectively, and can inflict even less damage. Delphox is also 3HKOed by Muddy Water, and Greninja is 2HKOed by Thunderbolt. Sliggoo has a losing matchup against Chesnaught, though, which 3HKOs faster with Brick Break.
Gym #7 - Olympia (Anistar City, Psychic-type): An Eviolite Sliggoo can manage to win against Sigilyph with Thunderbolt, a natural 2HKO; if Sigilyph puts up Light Screen, however, the move will turn into a 3-4HKO. This is still better than Sigilyph's 5HKO Psychic, but its Air Slash may prevent Sliggoo from hitting on occasion, thereby requiring healing. Sliggoo should also be able to defeat Slowking, though that depends on move usage and the timing of Olympia's healing items: Thunderbolt 3HKOs, but 4HKOs after one Calm Mind, and Slowking's Yawn can delay Sliggoo's sweeping. As Slowking is slower than Sliggoo and has no Water moves, Sliggoo can resort to Rain Dance to pre-emptively cure sleep induced by Yawn; Slowking also knows no Water moves, therefore it will not be advantaged by Sliggoo's rain. Considerations similar to Slowking hold for Meowstic, also 3HKOed but by Dragon Pulse, and 4HKOed after a Calm Mind; in this case, however, Sliggoo is outsped, and its chances of dealing significant damage are considerably lower. Sliggoo should preferably not fight Meowstic, especially if already weakened. On the other hand, an already evolved Goodra is more capable of standing up to Meowstic, averagely 2-3HKOing without any Calm Minds; Psychic can only 2HKO Goodra starting at +3 or above, and only at +4 the 2HKO becomes certain.
Lysandre battle #1 (Lysandre Labs): Sliggoo's Dragon Pulse is a 2HKO against Mienfoo, and Mienfoo's High Jump Kick is unlikely to 2HKO if Sliggoo holds the Eviolite, even though Mienfoo might outspeed. Murkrow is simply 1-2HKOed by Thunderbolt; Pyroar is 2HKOed by Muddy Water. Sliggoo should never come close to Gyarados, which nearly OHKOs with Outrage. Goodra can take an Outrage unless its nature is detrimental to Defense, and Thunderbolt will OHKO Gyarados if Goodra holds the Expert Belt.
Aliana (Lysandre Labs): Sliggoo can 2-3HKO Mightyena and 2HKO Druddigon with Dragon Pulse. However, even with the Eviolite, Druddigon's Dragon Claw is almost an OHKO, and may off a Sliggoo with poor Defense. Goodra 1-2HKOs Druddigon if the Expert Belt is being held, but can still be OHKOed by Dragon Claw if its Defense is low (for example, hindered by an unfavourable nature).
Celosia (Lysandre Labs): Sliggoo 2-3HKOs Manectric with Dragon Pulse; it can also 3HKO Drapion with the same move, though Drapion is also capable of 3HKOing with Poison Jab, notwithstanding the Eviolite. Goodra is also 3-4HKOed by Poison Jab on average, but is near-certain to 2HKO Drapion with Dragon Pulse; only Drapion's Acupressure can change the matchup, depending on the boosted stat(s).
Bryony (Lysandre Labs): Sliggoo 2HKOs Liepard with Dragon Pulse, but cannot fight Bisharp, which would 3HKO with Iron Head even with the Eviolite. Goodra 2HKOs it with Flamethrower, and has considerable OHKO chances with the Expert Belt.
Mable (Lysandre Labs): An Eviolite Sliggoo can 2HKO Houndoom with Muddy Water, but gets 2-3HKOed by Weavile's Ice Shard. Goodra can beat Weavile as well, 2HKOing it with Flamethrower.
Xerosic (Lysandre Labs): Sliggoo 2-3HKOs Crobat with Thunderbolt bt needs to avoid Malamar, whose Contrary and Superpower combination would overwhelm it, even with the Eviolite attached. Goodra can outspeed and 2-3HKO Malamar with Dragon Pulse, instead.
Lysandre battle #2 (Team Flare Secret HQ): Goodra cannot win against Mienshao, which 2HKOs with High Jump Kick; although a Protect gamble is possible on the first turn, and will win Goodra the matchup if successful, a Swords Dance would ruin the plan and turn Mienshao into a threat for the whole team. Honchkrow is highly likely to be OHKOed by Thunderbolt, if Goodra holds the Expert Belt; Pyroar is averagely 2HKOed by Muddy Water, though a Goodra with particularly high Special Attack may net the OHKO with a high damage roll. Thunderbolt OHKOs Gyarados as well, but Gyarados' Outrage has a small OHKO chance in turn; since Goodra's base Speed is almost the same as Gyarados', Goodra with a Speed-boosting nature are likely to win without risks, whereas Goodra whose nature is detrimental to Speed should avoid this matchup.
Xerneas (Team Flare Secret HQ, X only): Goodra may tank one Moonblast, but cannot damage Xerneas much in return. This matchup should be avoided.
Yveltal (Team Flare Secret HQ, Y only): Yveltal's moveset is entirely special, and Goodra's special bulk is excellent. Thunderbolt is an average 3HKO, even counting Yveltal's likely recovery through Oblivion Wing; if Thunderbolt is Disabled, Goodra can switch to Dragon Pulse, but it will be slightly less powerful than Yveltal's Dark Aura-boosted Dark Pulse.
Lysandre battle #3 (Team Flare Secret HQ): Mienshao 2HKOs Goodra with High Jump Kick, and should not be fought, as even predictive play through Protect can be foiled by a first-turn Swords Dance. Honchkrow is highly likely to be OHKOed by Expert Belt-boosted Thunderbolt, and Pyroar is 2HKOed by Muddy Water. Goodra is powerless against Mega Gyarados, which OHKOs with Outrage.
Professor Sycamore (Couriway Town): All of Venusaur's moves are Grass-typed, so a Sap Sipper Goodra can stall for the first six turns to max out its Attack and make the rest of the battle even easier with Return. Hydration Goodra can still 2HKO Venusaur with Flamethrower, whereas Charizard and Blastoise are 2HKOed by Thunderbolt; all three require the Expert Belt.
Shauna (Route 19): While Delcatty knows Play Rough, it only 3HKOs Goodra, which can 2HKO Delcatty with Dragon Pulse. Shauna's Goodra cannot 2HKO either, and Goodra can do so with Expert Belt-backed Dragon Pulse. Shauna's starter can also be 2HKOed by Flamethrower if Chesnaught, Muddy Water if Delphox, and Thunderbolt if Greninja; Delphox may lengthen the battle by spamming Calm Mind, but it can only outdamage Goodra at +2 or higher, at which point it will have taken significant damage.
Tierno (Route 19): Talonflame is highly likely OHKOed by Thunderbolt if backed by the Expert Belt, and even if not, Goodra can take two Acrobatics or one Acrobatics after a Swords Dance. Roserade is 2HKOed by Flamethrower, and only knows Petal Dance, which makes it completely harmless against Sap Sipper Goodra; Crawdaunt is OHKOed by Thunderbolt, once again given the Expert Belt.
Trevor (Route 19): Raichu gets 2HKOed by Dragon Pulse, Aerodactyl is 2HKOed by Thunderbolt. Florges should not be fought, as it easily 2HKOs with Moonblast and Goodra's Sludge Bomb is highly unlikely to net the 2HKO.
Gym #8 - Wulfric (Snowbelle City, Ice-type): Abomasnow is slower than Goodra, and easily offed by Flamethrower; Cryogonal is also 2HKOed by the move, if Goodra is holding the Expert Belt, and Goodra can take two Ice Beams from it. Goodra must avoid Avalugg, which can take a Flamethrower and respond by OHKOing with Avalanche.
Rival (Victory Road): Meowstic is 2-3HKOed by Dragon Pulse, and Altaria is 1-2HKOed, or OHKOed by Ice Beam; Absol may be 2HKOed too, but its Swords Dance and Night Slash combination are deadly to Goodra if a critical hit is scored, which is highly likely due to its Super Luck. Jolteon and Flareon are OHKOed by Earthquake, whereas Vaporeon is 2HKOed by Thunderbolt; the Expert Belt is required to secure this. All starters are 2HKOed: Chesnaught by Flamethrower, Delphox by Earthquake, and Greninja by Thunderbolt.
Elite Four Wikstrom (Pokémon League, Ironworks Chamber, Steel-type): Klefki's Dazzling Gleam is relatively weak, scoring only a 3HKO against Goodra; Flamethrower and Earthquake are both 1-2HKOs with the Expert Belt, and which move deals more damage depends on Goodra's nature and stats. Probopass would be OHKOed by Earthquake if not for Sturdy, but even its strongest moves deal little to no damage to Goodra; Scizor is easily OHKOed with Flamethrower. Goodra can either 2HKO Aegislash-Shield or OHKO Aegislash-Blade with Earthquake, and in either case, it can more than take an Iron Head from the offensive form; it needs the Expert Belt to secure the 2HKO against the Shield, though.
Elite Four Malva (Pokémon League, Blazing Chamber, Fire-type): Hydration Goodra should run Rain Dance and Muddy Water or Aqua Tail in this matchup, as the rain-boosted Water moves can OHKO all of Malva's Pokémon (Torkoal is only OHKOed by Muddy Water, however). Sap Sipper sets can still 2HKO Pyroar, Torkoal and Chandelure with Earthquake, with an OHKO chance against the first and third if the Expert Belt is being held; Talonflame can be 1-2HKOed with Thunderbolt.
Elite Four Drasna (Pokémon League, Dragonmark Chamber, Dragon-type): Dragon Pulse 1-2HKOs Dragalge and OHKOs Druddigon, if Goodra is holding the Expert Belt; Altaria and Noivern are OHKOed by Ice Beam regardless. Goodra is safe in this matchup, as none of Drasna's Pokémon can 2HKO it without scoring at least one critical hit.
Elite Four Siebold (Pokémon League, Flood Chamber, Water-type): Thunderbolt 1-2HKOs Clawitzer and, with the Expert Belt, OHKOs Gyarados; neither Pokémon can 2HKO Goodra. Starmie is naturally 1-2HKOed by Thunderbolt as well, but may put up Light Screen to increase its bulk; even then, Dazzling Gleam is still severely outdamaged by Thunderbolt, which still results in a 2-3HKO. Barbaracle can be either 2HKOed with Thunderbolt or OHKOed with Power Whip, if Goodra knows the move.
Champion Diantha (Pokémon League, Radiant Chamber): Hawlucha is 1-2HKOed by Thunderbolt or Ice Beam; the OHKO chances are higher with the Expert Belt. Tyrantrum is OHKOed by Dragon Pulse, though Goodra needs to outspeed to stay safe, as its Dragon Claw comes close to OHKOing; this should not be a problem in general, though Speed-lowering natures may make the matchup unfavourable. Similarly, Goodra can 2HKO Aurorus with Power Whip and is guaranteed to outspeed, but Power Whip has imperfect accuracy and Aurorus' Blizzard can also 2HKO (but is not guaranteed to do so). Gourgeist is 2HKOed (with a small OHKO chance, holding the Expert Belt) by Ice Beam, but can leave a parting shot with Trick-or-Treat and Phantom Force if it outspeeds; this significantly dents Goodra's health, up to thereabouts of 80%, but Goodra that do outspeed will only need to worry about Shadow Sneak, which is weak even if Goodra's typing is changed to Dragon/Ghost. Goodra can 2HKO Diantha's Goodra with Dragon Pulse and the Expert Belt, and the enemy Goodra cannot 2HKO back unless Goodra's own Special Defense is low. Goodra cannot stand up to Mega Gardevoir: it outspeeds and 2HKOs with Moonblast, and Goodra's chances of 2HKOing with Sludge Bomb are too low.
Goomy's initial moveset consists of Dragon Breath, Rain Dance, Flail and Body Slam. The moves it learns at earlier levels are generally not worth relearning; Dragon Breath serves its purpose as general Dragon STAB for a good while, in absence of Dragon Pulse, and both it and Body Slam have a nice paralysis chance, which does wonders to Goomy's slowness if it occurs. Rain Dance is a good strategic move for Hydration Goomy, but will provide negligible support to Sap Sipper carriers. Goomy learns Muddy Water at level 38; there is then the option of waiting until level 42 to evolve, to get Dragon Pulse early, or go with evolution at the earliest possible point in time and wait until 47 as Sliggoo for the same move. Both alternatives work out: Eviolite Goomy is not that frail, though it will require more care during its last few levels as an unevolved Pokémon, and Sliggoo can still hold its own with Dragon Breath until the better alternative rolls around. It should be noted that neither Goomy nor Sliggoo learn further moves by level, thus Sliggoo should be evolved into Goodra as soon as possible, and as soon as level 50 if its stats and moveset are predominantly physical, as Goodra learns Aqua Tail at that level. This move is especially useful for sets based on Rain Dance and Hydration. Goodra then gets Power Whip at level 55, which is preferable to Aqua Tail on non-rain sets, but otherwise Aqua Tail will work better; Outrage comes at 63, and can be considered over Dragon Pulse for physical sets, though for special or mixed ones it will be significantly less powerful, and locking Goodra into Outrage is bad for its sake either way, should a counter come up in front and sweep it off its feet.
Goodra's TM pool is excellent on the special side, and decent on the physical one as well. Specially speaking, all three elemental beams are available: Flamethrower, Thunderbolt and Ice Beam. Dragon Pulse should generally be preferred to Ice Beam due to STAB support, but Ice Beam will deal more damage to the dual Dragon/Flying-types in the late game. Their respective less accurate alternatives are available too, but among them, only Fire Blast is really reliable enough to be considered; an exception is made for Thunder on a Rain Dance-based Goodra. If the team desperately needs coverage against Fairy-types, Goodra can be taught Sludge Bomb or Sludge Wave as well, though it will obviously generally not want to fight Fairy-types at all; it can, however, tank non-STAB Dazzling Gleam and Moonblast well, thanks to its amazing special bulk. Similarly, Focus Blast is an option for more coverage, but generally outclassed by more accurate moves. On the physical side, Earthquake is a good move to have for general purposes, and Rock Slide complements its coverage well.
Standard: Dragon Pulse, Thunderbolt, and any two between Ice Beam / Flamethrower / Earthquake
Steel-types: All three of Goodra's weaknesses are resisted by Steel, which can also deliver super effective hits to one of them. Goodra's pure Dragon-type goes very well with any STAB Steel user, bearing in mind that dual Steel-types should preferably not have a secondary typing that negates their resistance to Ice, Dragon, or Fairy.
Ice-types: Ice is the type that covers the two main weaknesses of all Dragon-types best, and only second to Steel as far as complementing Goodra goes. While Ice-types are not exceedingly common in Kalos, several are easily available to the player.
Minimum stats are calculated with 0 EVs, IVs of 0, and a hindering nature, if applicable.
Maximum stats are calculated with 252 EVs, IVs of 31, and a helpful nature, if applicable.
Goomy Line Ratings
What Nature do I want? Quiet is the best choice, as Goodra will not do much with its own Speed and denting it will result in negligible hindrance. Modest is also great, though it will somewhat nerf its physical attacking capabilities. Any nature lowering the defensive stats, or Special Attack, is automatically bad; whatever lowers Speed or Attack is workable, and usually good.
Which Ability do I want? Neither of them is particularly useful or terrible, but Hydration will work best with Rain Dance sets. Sap Sipper, however, can do great with well-timed switch-ins.
At what point in the game should I be evolved? Whenever possible. Goomy should be a Sliggoo before Valerie, but will likely not see much use in that battle; the evolution can be delayed up to until level 42, if Sliggoo must learn Dragon Pulse early. It is appropriate to have Goodra around the time Olympia is fought, or not too long after that, and it can serve well in the Anistar gym if fully evolved.
How good is the Goomy line in a Nuzlocke? One does not simply spell "Goodra" without "good". It has great special bulk and can take virtually any hit, even critical hits, thanks to their nerfing in the Kalos generation. Goodra can face basically any special hitter without fear, and can deal well with physical hitters as well, providing their moves are not super effective against it and/or that their Attack is not over the top. Training it as Goomy or Sliggoo will be hard, down to the very last level before the final evolution, but more than worth it.