Wear the Blue Hat:
Beat the game to unlock a blue hat for Parappa.

Wear the Pink Hat:
Beat the game with the blue hat to unlock a pink hat for Parappa.

Wear the Yellow Hat:
Beat the game with the pink hat to unlock a yellow hat for Parappa.

Enable the Song Test:
Beat the game with the yellow hat to unlock a new dog house that allows you to listen to any song in levels that you finished with a cool rating

Thanks to Revolution reader A Massive Toe!