This is one of the few products that it's rarely if ever necessary to replace a battery in, as the warranty will cover a rapidly draining or not-charging battery. I'm glad you didn't tear down your chime, too! ;)
Use a small straight-blade. Sounds odd, but works perfectly.
I think they rate it as "moderate" for needing to acquire the "Y" type screwdriver, but, (and here's a protip for first timers...) A small straight-blade actually fits and turns the screw as normal, with no need for special tools. :)