How do you open the Dark Palace without paying Kiki?

The first dungeon in the Dark World is the Dark Palace, as you approach the Palace a little monkey-type creature called Kiki starts following you, if you give him 10 rupees. Once you get to the entrance to the Dark Palace he offers to open it for you for 100 rupees.

You are also given the opportunity during this conversation to "try and do it yourself". Is it possible to open the Dark Palace without paying Kiki rupees, if so - how would you achieve this?