Unlockable: Samurai Sword & Death Scythe

If you complete the game with and A or S rank you will start with the Samurai Sword and Death Scythe if you start a new game from that save file.

Unlockable: Unlimited Throwing Weapons

Complete the game with 9,999 Purple Fragments and you will have unlimited throwing weapons when you start a new game from that save file. You must, however, find a throwing weapon before you can use it.