Henry is unlocked in the Monorail Meet event, as stated in the achievement description. The event is a 9-hole match play event versus Henry. Henry gets 2 uses of his special ability, like you. His ability splits the ball into 5 parts, and he gets the best lie of the 5. He's pretty easy to beat, as he continually comes up short on many shots and rarely lands close to the hole before shooting for bogey. Don't be over-aggressive, and play for par. You'll win quickly.