Am I the only person struggling with the grip part of the mini game? I keep slipping off which causes me to have to destroy the legs off them again. Its driving me absolutely crazy, is there anything I am doing wrong other than not being able to hit the button fast enough?

Go for the tail instead of the head.  Just jam the button it tells you to hold on for the tail, open the first hatch, jam another button for grip, go over to the other side, open the other hatch, and wiggle the stick back and forth to kill the Watcher.  The hardest part by far is avoiding getting chewed up by the auto tracking gun when going for the legs.  The minigame is cake.