I don't have a Glo HD so I don't have first hand experience with opening it. I think the back cover simply pops off... battery should have a simple connector, of course you have to be careful with it...
Letting the battery run empty by itself... it might take a very long time [esp. if you left the charger cable connected for a while] and it's not good for the battery...
like this?
https://www.youtube.com/watch?v=lAbwMZ83lcM this is about replacing the Sd card but you can also see battery with black+red cable and white connector, just be very careful when pulling it up/out of its socket. I managed to break this connector on the old Glo... thin fragile plastic and all that