Four fragile plastic clips hold the casing together. You can see their locations more clearly in this guide.

The clips help hold the seams together. If you break these clips, the controller will still work.

Beginning with the left handle:

Pinch the left handle of the controller to introduce an opening.

Wedge a plastic opening tool into the opening and slide it up towards the joystick.

Pull down on tool to pry open the casing.

Repeat these steps for the right handle.