Espeon is a pretty cool Pokemon, having the ability to run a lot of sets. The main one is obviously Shell Smash though
Espeon @ Fist Plate / Insect Plate
Trait: Magic Bounce
EVs: 252 Spd / 252 SAtk / 4 HP
Timid Nature
- Shell Smash
- Psystrike / Stored Power
- Judgment
- Signal Beam / Shadow Ball / Lovely Kiss
This set is pretty simple, Shell Smash and Sweep. Espeon is probably the best Special Shell Smasher in the tier thanks to Magic Bounce and it's stats. Magic Bounce lets it avoid Taunts and Statuses that haunt the others while letting Espeon support its team a little. Psystrike is the best Psychic-STAB available, and it lets Espeon beat the blobs. Stored Power is stronger after a Smash, but Psystrike lets it hit before a smash. Judgement is the best coverage move for Espeon, especially with the Fist Plate. Signal Beam is the third move, since I think it's better than Shadow Ball since it hits the same things with roughly the same power, except it wrecks Celebi, whom could be a problem with Heart Swap + Baton Pass. Lovely Kiss is also an option here, as it lets Espeon put counters to sleep. It also gives it a chance against Sableye if it gets lucky with Sleep Turns. This, however, requires an Insect Plate. Insect Plate Judgement is an option for hitting Psychic-types while still hitting Dark-types if you choose to run Lovely Kiss. You miss out on Steel-types though, so that might not be desirable.
Another interesting set is a full support one, as Espeon has an excellent support movepool. Dual Screen has been mentioned and I think it's pretty good.
Espeon @ Light Clay
Trait: Magic Bounce
EVs: 252 Spd / 252 HP / 4 SAtk
Timid Nature
- Reflect
- Light Screen
- Psystrike
- Healing Wish / Lovely Kiss / Softboiled / Baton Pass
Simple set, Dual Screens and Psystrike for STAB. The last three depend on the team. Healing Wish is good for Offensive Teams in the later game, bringing a sweeper back from the brink of death. Lovely Kiss lets Esepon cripple threats, which is good early-game. Softboiled lets Espeon last longer and set up more screens. Baton Pass lets Espeon escape Pursuit. An EV spread of 252 Spd / 252 SAtk / 4 HP can be used, but Max HP is better imo.
Finally, Espeon now has a reason to be used on Sun Teams over Xatu, using the following set.
Espeon @ Focus Sash / Flame Plate
Trait: Magic Bounce
EVs: 252 Spd / 252 SAtk / 4 HP
Timid Nature
- Hidden Power [Fire] / Judgement
- Copycat / Encore / Softboiled
- Psystrike
- Lovely Kiss
Focus Sash and Copycat here is used for a reason. Espeon comes in on a hazard setter like Forry or Skarm. If they attack, Focus Sash will make sure you survive their attack and either bring them down to Sturdy or kill them. If they are brought to Sturdy, then Espeon is dead, letting you bring anything to threaten it. Suddenly, Forry can't switch in on anything, meaning it will be almost impossible for it to set up hazards. Meanwhile, if it didn't predict Espeon and goes for Hazards, then you are free to use Copycat while they switch in fear of a potential HP Fire to set up hazards against your opponent. Copycat in general is a pretty cool choice, letting Espeon use moves that the opponent uses against them. Of course, if this is too gimmicky for you, Softboiled and Flame Plate Judgement are an option. Encore is also an option, as it gets similar results as the Copycat scenario above, but less gimmicky than Copcat. If neither is your cup of tea, then Softboiled is an option. For items, Flame Plate Judgement is an option, which has pseudo STAB in Sun and pairs nicely with Psychic STAB. Lovely Kiss lets you cripple something by putting it to sleep. This set should only be used on Sun Teams imo; any other team is better off using either a Baton Pass set or the Dual Screen set.