A:Answer 1. Pop off the cover.
2. Press down on the two plastic tabs just above the batteries and this releases a small plastic holder which you then just slide completely out and set aside. (This is probaby the step you were understandably missing because the tabs are small-ish and their purpose isn't documented or readily apparent)
3. With thiis holder out of the way, the batteries have plenty of clearance and can be removed by hand.
4. Replace the batteries, put the plastic clip back into place, reattach the cover, done.
Not hard but the holding clip is not obvious or inuitive and should at the very least have been documented in the guide. It's a nice little mouse though, I'm happy with it, and hope this helps someone.