This is a decent guide. Thank you to the author! Problem is that they don't make these devices user serviceable, so we basically have to pry and force the cap off. ARGH! RIGHT TO REPAIR NOW!!

Photo here is unclear, but there are two small black posts on the circuit board that the rubber cover needs to line up with. Gently press down on the cover, and be sure that the side clips (of the rubber cover) and engaging the sides of the circuit board.

Cover the toothbrush with a thin towel or some cardboard, then take a pair of pliers or channel locks and squeeze the corners to slightly deform the case. That will give you some room to get under the cap.