The most challenging part of the axel (whether on ice or off ice) is the timing and technique of getting over your landing side in the air.
The exercise that helped me get my axel on the floor was this one: Stand in front of a secured bench or raised platform. Take off just like an axel or waltz jump and do just 1/2 turn, landing backward on your right foot (assuming you jump CCW) in an open backspin position. That means your shoulders and hips are squared, your arms are rounded in front of you, and your left foot is in front of your right shin. Practice this until you can land backward in this position with control and balance. Once you can do that, do the same thing on the open floor, but pull in once you are backward in that position. That's your axel.