Complete the game and after watching the whole credits you can make a new save. After that you can select the Bitter difficulty along with your old equipment.

To unlock the minigame "Pure White Giant Glastonbury", beat the Rank 04 battle. To play it, go back to the motel and select your TV. The game can be played from there.

To see the true ending, complete the game with all beam katanas obtained. If you do not have them all by the end of the game, choose to return to Santa Destroy, obtain them, and return to a bathroom to view it.

Beat the game and you will unlock a new shirt.

After defeating the game on any difficulty, save your game when you're prompted to and then load that save up. Choose a difficulty and you'll start a New Game+. You'll retain all the money you had left over from your previous playthrough as well as all clothes you found and bought. All jobs and missions will be available and some new shirts will be available at Area 51.