Unlock Harder Dificulty:
Beat the game once to unlock a harder difficuly setting.
Unlock All Artwork:
Beat the game once to unlock all artwork.
Unlock Master Ninja mode:
Beat the game on hard to unlock Master Ninja mode.
Unlock Muramasa's prize shop:
Beat the game once on Normal to unlock Muramasa's prize shop.
Unlock Master Konutichi mode:
In the forest of shadows, as Momiji, at the end of the chapter you will have to fight a dragon. Defeat the dragon (on any difficulty) and you will unlock a difficulty called 'Master Konutichi' where you play as a hidden ninja named Rin.
(supplied by: masteraustin)