I give up. I need to know how. Would someone be able to provide a sound strategy to achieve this?
Assuming you have already gotten to the sphinx's back where you could take the comet and complete the level, you need to go past the comet and enter the back of Yoshi's head.
Inside you will eventually find an area with 2 rooms, the left of which has 2 small holes on its left, covered by cardboard. These are Yoshi's eyes. Use the hammer on the left side of the right room to knock the wall down, then climb it to get to the eyes. Hammer the eye cardboard, walk out, and be prepared for a fight.
The fight's kind of a beach.