Indeed, a glasses screwdriver would probably be your best bet. If you still can't get it open, I would suggest actually going to the jewelry department of Walmart or anyplace that has jewelry and ask if they could open it for you. They'll usually do this for free.
Part of the reason you may be having problems opening it is the battery may have, unfortunately, corroded inside. There is usually a plate blocking the gear work from the battery just in case of this, so all should still be good!