You will need to find another way around the back to get to that chest.
Here are some pointers that should help you get through the rest of the dungeon:
- the platforms held by four chains can be swung using the ball chain, use the swining motion of the platforms and correct timing to get across them.
- refer to your map often so you know where you're going.
- towards the end you will figure that you need to transfer a cannon ball through a series of rooms to a particular cannon. Use the switches on the walls to help you do this.