Amazing Island is a 2004 video game developed by Ancient and Hitmaker and published by Sega for the Gamecube. In the game, you are sent to a fantasy island where you create monsters compete in various courses of minigames. The draw of the game is its monster creator, which can generate monsters for you or allow you to create them yourself. It also features premade monsters in the form of "monster cards" you can collect.
The composers for the game, Yuzo Koshiro and Motohiro Kawashima, also composed for Streets of Rage and Etrian Odyssey.
My Monsters 
Fanart
Monster Cards
Click on the icons to the left!