Gladion (Route 5): Sylveon can 2-3HKO Zubat with Swift. Type: Null's Tackle is about as strong as its Fairy Wind, averaging at a 5HKO, so Sylveon can win if healed once, or deal damage until it needs to be switched out and let a teammate finish the job. Alternatively, Sylveon may use Reflect to reduce Type: Null's damage.
Totem Wishiwashi (Brooklet Hill): Sylveon does fairly well in this matchup, nearly matching Wishiwashi's rain-boosted Water Gun in damage with its own Draining Kiss. Both moves take four to five turns to KO. The most damage Sylveon can take is from a Helping Hand, rain-boosted Water Gun from the Totem, but that still reaches only the 3HKO range at best; with just a little healing, or possibly none if the Draining Kiss recovery is good enough, Sylveon can win.
Battle Royal (Royal Park): Sylveon's good endurance makes it an excellent choice for the Battle Royal. With Draining Kiss, it can stand up to any opponent, although Hau's Torracat does dent it significantly with Fire Fang, an average 4HKO. Since Rockruff is damaged the most by Draining Kiss, which results in a 2HKO, it should be targeted; this will help Sylveon keep its health high until the first kill is scored.
Totem Salazzle (Wela Volcano Park): Sylveon can chip away roughly half of the totem's health with Swift-based Breakneck Blitz, but should switch out afterwards, if the totem opens with Toxic. The ally Salandit's Venoshock is a 2HKO if Sylveon is poisoned, and the residual poison damage plus Salazzle's Flame Burst can end Sylveon in a single turn. Light Screen can mitigate this risk, but critical hits are likely to kill Sylveon even in high health.
Totem Lurantis (Lush Jungle): Sylveon is poorly suited for this battle; Lurantis can 2HKO it with Solar Blade, which takes three turns instead of four with its Power Herb, and with Trumbeak's Pluck or a high Rock Blast roll it may be killed even in a single turn. Even Reflect can only help so much; do not use Sylveon here.
Plumeria (Akala Outskirts): Swift can 4-5HKO Golbat, which is not dangerous due to not having any Poison moves; with Swift-powered Breakneck Blitz, only three turns are needed to KO. Salandit also lacks Poison moves outside of Poison Gas, and can be 3HKOed with regular Swift.
Olivia (Ruins of Life, Rock-type): Nosepass' full Special Defense EV investment makes it tough to beat; Sylveon's Draining Kiss outdamages its Rock Slide, but both moves require several turns to KO. Boldore is 3HKOed, but Sylveon's health needs to be high to prevent five-hit Rock Blast turns from killing; Reflect is good to have, to mitigate this risk and reduce damage. Sylveon can also win against Lycanroc, but should once again be supported by Reflect, since its Continental Crush chips away up to around 80% of its health and Draining Kiss recovery alone - with the move being a 4HKO - is not enough to compensate.
Lana (Konikoni City, Water-type, optional): Chinchou and Shellder are respectively 3HKOed and 2-3HKOed by Draining Kiss. Sylveon should set up and maintain Light Screen until at least the first turn in which Araquanid is called into battle, and then renew it along the way; Araquanid's Bubble Beam is stronger than Sylveon's Draining Kiss, and Hydro Vortex in particular can chip away up to almost half of Sylveon's health. With Light Screen up, however, Sylveon easily outdamages it.
Kiawe (Royal Avenue, Fire-type, optional, Sun only): Sylveon can outdamage Growlithe's Fire Fang with Swift, but it is still recommended to use Reflect first, since all of Kiawe's Pokémon are largely or entirely physical hitters. Fletchinder is relatively easy to beat, once again with Swift; Breakneck Blitz can finish it from half health or a little over that. While helpful against Growlithe and Fletchinder, Reflect becomes absolutely necessary against Marowak, and must be kept up at all times; Marowak's Bonemerang is a 3HKO and Sylveon's Draining Kiss is really weak against it, being outdamaged even after Reflect is used. It is difficult for Sylveon to beat Marowak, though it may manage if Draining Kiss deals enough damage and provides enough recovery to take Marowak's hits.
Mallow (Lush Jungle, Grass-type, optional, Moon only): Draining Kiss is a 3-4HKO against Phantump, unless it uses Leech Seed; the move can increase the amount of turns needed to beat it, though Phantump's direct attacks are no issue. Similarly, Shiinotic can at best use Mega Drain against Sylveon, but also knows Ingrain and Sleep Powder. Steenee is the easiest to beat, plainly 2-3HKOed by Sylveon's STAB.
Nihilego (Aether Paradise): No. Even though Light Screen can help reduce the Venoshock damage, Sylveon's moves are all resisted and do next to nothing to Nihilego.
The hatched Eevee starts with the standard Growl, Helping Hand, Tackle and Tail Whip. Tackle has been downpowered, but is still good for training, especially on Eevee with Adaptability. Sand Attack comes at level 5, and is better than Helping Hand, but not by much. At level 9, Eevee learns Baby-Doll Eyes, and this is the earliest point in the game at which it can evolve. There is no reason to delay Eevee's evolution into Sylveon, since none of Eevee's level-up moves are particularly interesting for Sylveon to learn: at level 13, both the unevolved and the evolved form learn the relatively useless Quick Attack; at level 17, both learn Swift, and Eevee also gets Bite, but Sylveon has no use for a low power physical move. Sylveon should, by all means, be evolved by level 20: at that point, Eevee gets Refresh, while Sylveon learns the much more useful Draining Kiss. Upon evolving, no matter the level, Sylveon gets Fairy Wind, but Draining Kiss is better in both power and effect, since it helps Sylveon regain health. At level 25, Eevee gets Take Down while Sylveon learns Skill Swap, neither move should be kept for the long term; at level 29, Eevee learns Charm and Sylveon learns Misty Terrain: again, Sylveon's alternative is significantly better than Eevee's, though other moves will help even more than Misty Terrain. At level 33, Eevee gets Baton Pass, the only possible reason for anyone to not evolve Eevee into Sylveon early. In any case, Sylveon is not the best Baton Pass user there is; there are better ones even among its Eeveelution cousins. Sylveon, instead, learns Light Screen at level 33, though the move is also accessible by TM at a much earlier point in the game. Level 37 once again proves the evolution should happen early: Eevee gets Double-Edge while Sylveon gets its best available STAB, Moonblast. Since the Move Reminder is only shortly before the League, Sylveon must absolutely learn this move. At level 41, both Pokémon get the disappointing Last Resort, and at level 45 they learn their last level-up move: Trump Card for Eevee and Psych Up for Sylveon, neither of which warrants a moveslot.
Sylveon's level-up movepool is not bad, and can be further expanded with TMs. Shadow Ball and Psyshock both add to its coverage, and the latter also permits it to hit enemies hard even if their Special Defense is high; however, Psyshock comes somewhat late during the game. Calm Mind is an excellent pick; it allows Sylveon to invest on its special power and bulk simultaneously, making it a very durable special tank. Reflect and Light Screen also play a great defensive role when used by Sylveon. Dazzling Gleam would be a good Moonblast alternative, but in these games, Moonblast comes around before the Dazzling Gleam TM does, rendering it useless.
Eevee's Breakneck Blitz can be very powerful in the early game, especially if used by Adaptability carriers; however, evolving Eevee early is generally more than worth forgoing the Z-move. Sylveon makes great use of Twinkle Tackle, but the Fairium Z is unfortunately available only in the late game. Through its TM coverage, instead, it gets access to Never-Ending Nightmare and Shattered Psyche.