Once you have the battery compartment on the side, take all the stuffing out.

Under the battery compartment, there will be another compartment held in place inside a cloth bag. This will be the button compartment.

Carefully cut the cloth covering the button compartment around the edges.

To avoid damaging cables within the button compartment, you can pinch the excess cloth on the sides and begin your cut there.

Remove the button compartment and set it aside.

NOTE: The button compartment from my LeapFrog was completely ruptured from the battery compartment.