At the Main Menu, hold R1 and enter the following:

Double punch damage:
Right, Down, Left, Up, Left, L1.

Double speed boxing:
Down, Left, Down, Up, Right, L1

All default boxers and arenas:
Right, Down, Up, Left, Up, L1

All default boxers, arenas, and Rocky Statue:
Right, Right, Right, Left, Right, L1

All default boxers, arenas, Rocky Statue, and Mickey:
Up, Down, Down, Left, Left, L1

Full stats in tournament and exhibition modes:
Left, Up, Up, Down, Right, L1.

Full stats in movie mode:
Right, Down, Down, Up, Left, L1

Win fight in movie mode:
Right, Right, Left, Left, Up, L1. Now press L2 + R2 during a fight in movie mode to automatically win.

Thanks to Revolution reader Shmit!