The following items become available for purchase in Rodin's shop when you complete the corresponding task.
Unlock Immortal Marionette:
Complete the game on the Very Easy or Easy difficulty.
Unlock Bangle of Time:
Complete the game in under 3 hours on Normal or higher difficulty.
Unlock Eternal Testimony:
Get 50 Umbran Tears Of Blood.
Unlock Climax Bracelet:
Get 101 Umbran Tears Of Blood.