This little sidequest involves everyone's favourite four-legged Pokemon with far too much evolution choice: Eevee. When you've got some spare time, head for the Akala Island Thrifty Megamart (not the spooky one), located in Royal Avenue.
Inside, chat to the Veteran behind the left-most checkout counter along the south side. Previously, he had nothing to say, but now that you're the Champion, he has a heartfelt request, which is find and challenge his old friends, the fabled Eevee Users.
Trouble is, he hasn't seen his friends for, what, 20 years? So he's not entirely sure where they are, besides an incredibly vague location. Fortunately for you, we've already done the hard work of tracking down all 8 of the Eevee Users.
- Vaporeon User (Water): Top floor of the Trainer's School, the old woman towards the east side.
- Flareon User (Fire): Tide Song Hotel, to the west of the reception counter
- Jolteon User (Electric): Malie City Community Centre, the woman sitting near the TV in in the lounge area
- Espeon User (Psychic): Geothermal Power Plant, the man in front of the TV.
- Umbreon User (Dark): Hau'oli Cemetary, man in the north-west corner (all day)
- Glaceon User (Ice): Iki Town, woman in kitchen in the south-western house
- Leafeon User (Grass): Hano Beach, swimmer in the north-most beach area (with the buried Pokemon).
- Sylveon User (Fairy): Seafolk Village, little girl in the north-east corner of the Steelix (east-most) ship.
Two Birds in One Stone
This sidequest will take you all over Alola. Therefore, it's a smart idea to do it simultaneously with other tasks, such as the "Clean Up" sidequests mentioned in the following pages.
Each Eevee User has an a single Level 54 or 55 evolved Eevee that matches their title. Honestly, you should have zero trouble defeating them, with your numerical advantage alone (6 versus 1, c'mon!).
Once you've met and defeated all 8 Eevee Users, return to the Veteran in Thrifty Megamart. To seal the deal, he asks for one final battle with himself. If you thought the previous battles were easy, this one is even easier since he uses a plain old Eevee.
After fulfilling his wish, you'll be given his prized Eevium Z, which transforms Eevee's Last Resort move into an exclusive Z-Move. It only works for Eevee and not any of its evolutions though--hey, gotta give Eevee an advantage somehow!