The following can be done while playing in either single player or multi-player mode. However, for the mode to become unlocked in multi-player, you must switch your players to the first slot.

Fourth MP Move: Increase your Blast Technique to about 1,000.
Hard mode: Successfully complete Normal mode; this applies to player one only. To unlock it for other players, switch them to the first slot.
Increase MP Power Moves: Keep repeating your MP Moves. Notice that the Tech Ups will increase about 300 tech points and you will level up your move from Petty to Magna.
Super Hard mode: Successfully complete Hard mode; this applies to player one only. To unlock it for other players, switch them to the first slot.