At the title screen press R1 Up L2 Down. Select a regular puzzle game and you'll have 27 more levels.
At the Options menu press Left Right R1 R2 L2 L1 Up Down. QUICKLY highlight Credits and press X.
Start a Puzzle game and when the map appears press Left Left Up Down then L1 L2 R1 R2. A character select screen will appear just select any player and X. Buddy will still appear on the map but your new player will be in the game.