Jump on the elevator nearby. He warns not to disturb him lest the platform go crashing down into the pit below. Power Slash him anyway and he will drop the controls, sending the platform down. You have to slash him a number of times before reaching an opening.
After jumping onto the land to the left, move past the Imp guard and into another cavern with more enemy Imps.
It's the jumping to the "land on the left" that causes problems for me. Every time I try, I fall just a few units short of making the jump. What am I doing wrong?