Complete Story mode to unlock these ninja sandles which will give you the ability after a few steps running to increase your run speed to roughly double your normal speed. To gain their bonus you must have them in your inventory on the mission.
Unlock Rikimaru's Unbreakable Sword: When you have collected ALL the scroll parts using Rikimaru his unbreakable sword will become available.
Unlock Ayame's Unbreakable Sword: When you have collected ALL the scroll parts using Ayame her unbreakable sword will become available.
Unlock Random Endless Items: Collect ALL the mask parts using Rikimaru to unlock three random endless items.
Unlock Oni Mask: Collect ALL the mask parts with Rikimaru and Ayame to unlock the Oni mask. Wear the Oni mask to use Onikage and if Rikimaru is equipped with a sword he will wield a large unbreakable sword that does a large amount of damage.
When you have completed a mission successfully Shadow mode will become an available option by pressing the 'Start' button at the Story mode 'Mission Select' screen. Shadow mode is a more difficult version of the missions you have already completed.