You can remove the side panels with a pry tool.

You don't need to remove the rubber. The rubber on this controller was already bad.

Remove the 5 Torx Security Bit (TR9) screws.

Pry the panel next to the 3.5mm port.

Be careful to not rip the ribbon shown in the next step.

Be careful to not rip the ribbon cable.

You can pop the connector up to remove the ribbon easily.

Ribbon Cable

Remove the 2 Torx (T6) screws.

Desolder the 4 wires on each side, these control the vibrations and the RT LT.

Pull up from the "top" side of the controller on the daughterboard.

Be Careful to not lose the sync button.

Pry the middle section up from the home button side.

This will also remove the LB and RB which is a single part.

Unscrew the 6 Torx (T6) screws.

Now you can remove the buttons themselves.