Instructions
Start the game, then select "Offline Mode" from the main menu.
Select any of the available game modes apart from the "Vs Battle." "Vs Battle" is a multiplayer mode and thus the person using the first controller will always wear the "1P" costume.
Use the left analog stick to highlight your character, then press one of the "Punch" buttons to use the "1P" costume for the fight. On Xbox 360, the "Punch" buttons are "X" and "Y" while on PlayStation 3, they're "Square" or "Triangle."