Go to the Main Menu (with the Thing's mug showing) and go to Options Menu. There, highlight the training bar and press all 4 trigger buttons at once (L1+L2+R1+R2). This will allow you to access the following items on the options screen: Invincibility, Level Skip, Unlimited Replay, and Big Boy (which lets you play a giant character or a tiny one)...
Pause the game and press select then go on choose character choose the character you want but be ready to pause On the second player Pad immediately after you have chosen. The same character will be available to choose if you was quick enough. :)