Activate cheats:
Go to the Options screen, Highlight training mode and press L1, L2, R1 + R2. You will now have the following cheats -

Level Select:
Turn this on then press L1, L2, R1 + R2 while playing the game. Up and Down will change levels, Triangle or X will select the level, Start will reenter the game.

Invincibility:
Just turn it on to be invincible.

Big Boys:
1: Characters are small
2: Characters are normal size
3: Characters are large

Freeplay:
Turn it on for loads of credits.

Clones:
While playing a two-player game, press Start, Select, then choose a different character, then press X. When either player is teleporting in the blue ray, have the other player press Start, then Select. If you're quick enough, both players will have the same character.

Extra Options:
Go to the Options screen then highlight Training and press L1 + L2 + R1 + R2 to get extra options like invincibility and level skip.