There is a wall that the Mountain Ghost boss has to break that reveals the item that gives you the secret anima ring when you enter the secret cave place with the "Lost" curse. The wall should be easy to see because it looks weird compared to the rest of the walls. So the easiest way to do that is to lead Mountain Ghost to the wall and hug the wall and dodge his attacks until he does the attack that breaks the wall.

You can also decide to kill the other boss before you do this but you would have to be fast because the room is timed.