Ninja Gaiden II -
Go across the top again, this time don't drop down. Once you get to the end, save and then climb the ladder. Do directly to your right and get the chest. Then get the scroll from the dead guy.
When you reach a big open area, kill all the black spider clan ninjas in the area then a large door will open up displaying a statue inside. Go up to the statue and take the lunar staff from it.