While at the Character Selection Screen, highlight a fighter and hold L2 and press X.

Big head with alternate costume

While at the Character Selection Screen, highlight a fighter and hold L2 and press Circle.

Small fighter

While at the Character Selection Screen, highlight a fighter and hold R2 and press X.

Small fighter with alternate costume

While at the Character Selection Screen, highlight a fighter and hold R2 and press Circle.

Large arms

While at the Character Selection Screen, hold L1 + L2 and select a character.  Alternatively, just beat the game on level 4+ without using a continue.

Large stage

Defeat ten consecutive opponents in Survival Mode.

Small stage

Beat the game on difficulty level 4 or higher with Greg.