You could try one of those gadgets that help to remove lids from jars maybe? I think there is a type that is like a band that wraps around the object and is tensioned to grip the object and a handle attached to make grip easier?
The battery compartment just needs a small flat screwdriver to pop the metal lid off and the batteries can then be removed easily and replaced. The lid slides away from the edge first before lifting.
There’s a few versions available online.