Walkthrough: After the Iki Town Festival and later going to meet the Professor at his lab, you will be encouraged to go visit and learn a little bit on battling at the Trainer's School off Route 1. Here, you will embark on a challenge to defeat a given number of trainers found at the school, followed by the teacher herself. After defeating all of them, you will meet the one and only Trail Captain on Melemele Island, Ilima.
Wild Pokemon:
Initial Pokemon (Levels 6-8): Magnemite(50%), Meowth(30%), Grimer(20%)
Trainers:
Youth Athlete Hiromi - Level 8 Pikipek
Preschooler Mia - Level 7 Bonsly
Youngster Joey - Level 7 Metapod
Rising Star Joseph - Level 8 Grimer
Teacher Emily - Level 8 Magnemite, Level 9 Meowth
Items:
Potion - Left of Front Door
Quick Claw - From girl in back of building
Antidote - South of Youngster Joey
Paralyze Heal - South of Youngster Joey
Great Ball x5 - Defeat Teacher Emily
Flame Plate - Near top right furnace (hidden)
Great Ball - Middle of Battlefield (hidden)
Potion - From child in classroom
TM01 (Work Up) - Defeat Rising Star Joseph
King's Rock - Defeat Principal Asuka (Post Game)
After Defeating Kahuna Hala
Details: After defeating Kahuna Hala, you can return to the Trainer's School and have a Rematch with Captain Ilima before leaving Melemele Island.
Captain Ilima - Level 15 Gumshoos w/Normalium Z, Level 14 Smeargle
Post Storyline
Details: After defeating the storyline much later in the game, you can return to the Trainer's School and Battle a few New trainers, including the Vaporeon User (Eevee Quest) and Principal Asuka.
Trainers:
Black Belt Duane - Level 55 Primeape, Level 56 Lucario
Principal Asuka - Level 57 Granbull, Level 57 Stoutland, Level 57 Arcanine
Vaporeon User Polly - Level 55 Vaporeon