Zettai Shougeki: Platonic Heart

Walking home from school Aya Iseshima stumbles upon a brutal brawl between two girls fighting over something called the "Platonic Heart". Being a martial arts master herself Aya interferes in the fight to break it up. Afterwards Aya befriends one of the fighters and finds out the Platonic Heart is a jewel that can grant one wish for any girl that posseses it and there is a battle royal tournament going on for its control. Unfortunately for Aya it seems her interference has now registered her as a participant in the fight and it looks like there's no way out but to win.