To walk through a floor, equip two Heart Refreshes and a Duplicator. Start to jump through an open doorway and right before you go through use a Heart Refresh. Then, activate the second Heart Refresh. While the second Heart Refresh is activated, press the button for the first one repeatedly. You should start to go underground.
After using this trick, you can access a hidden save room. Go towards the drawbridge and you will fall into a hole that leads to an underground cavern. Go to the right to access the save room.