Most character unlocking is done in Story Mode, but a few have to be bought in the Store. Difficulty does not matter when playing through Story Mode.

Character	How to unlock
Aku	Buy in Store for 1500 points.
Blossom	Beat Kids Next Door Theme in Story Mode.
Bubbles	Beat Kids Next Door Theme in Story Mode.
Captain K'Nuckles	Meet him in Stage 1 of FlapJack Theme in Story Mode.
Captain Planet	Beat Samurai Jack Theme in Story Mode.
Father	Beat Story Mode.
Grim	Beat Dexter's Lab Theme in Story Mode.
Him	Buy in Store for 1200 points.
Hoss Delgado	Buy in Store for 1200 points.
Johnny Bravo	Buy in Store for 1500 points.
Kevin 11	Buy in Store for 1200 points.
Mojo Jojo	Beat Story Mode.
Monkey	Save him in Stage 1 of Dexter's Lab Theme in Story Mode.
Samurai Jack	Beat him in Stage 1 of Samurai Jack Theme in Story Mode.
The Scotsman	Buy in Store for 1200 points.
Toiletnator	Buy in Store for 1200 points.
Vilgax	Beat Story Mode.
Young Ben	Buy in Store for 1500 points.