There is much to be explored, but make sure you get all the belts. There are 10 in total and some of them are hidden.
There are also weapons that can be used as items in battle. They're especially helpful against bosses, and there is a chest with some soon after starting.
Be ready to fight, and remember to be as fast as you can.
Eventually you'll find yourself in a hot steamy room.
Octo is here, and the Ninja Stars you found earlier will help a lot if you still have them. Defeat all eight tentacles to move on.