No order and as far as I'm concerned the Gym Battles are bosses.

YouTube - "Reason Boss Battle" - Shin Megami Tensei: Nocturne

YouTube - Favourite VGM - Wild Arms 3: Schrodinger Family

YouTube - Final Fantasy X Music - Seymour Battle

YouTube - Pokemon Red & Blue - Battle vs Gym leader (music)

YouTube - Zelda: The Wind Waker Music - Mini-Boss