Various bonuses are unlocked when you meet certain conditions, which include the following.

Accessing the fighter's stats as soon as a reward is offered (from the locker room).
Doing a certain number of taunts (at least one to three per match when safe enough).
Doing counter-moves.
Doing so many "Killer Moves", "Lethal Moves", or "H-KO"s in a match or series of matches.
Maintaining your popularity for a length of time.
Playing all the default players at least once (Aisha, Aigle, Makoto, Dixie, Reiko, Evil Rose, Benikage, Candy Cane, Miss Spencer, and Anesthesia).
Winning a number of matches without losing too much (winning streak of three).