Bonus world & puzzles
At the "Push Start Button" screen, press Triangle, Right, Left, Triangle. You should see an icon appear in the upper left corner of the screen once the code is entered. Select Puzzle Mode, then the "Arcade" option to access the additional puzzles.

Bonus characters
At the "Push Start Button" screen, press Triangle, Left, Right, Triangle. You should see an icon appear in the upper left corner of the screen once the code is entered.

Cheats