If you drop a Xbox 360 controller don’t let it land on it’s bumper buttons. The micro-switches break easily in the inside. They might still work but need more pressure to be triggered. This problem plagues old Sega Saturn gamepads too.
To open Xbox 360 controllers you need a special Torx security screwdriver with a hole in the tip, size T8H. If you don’t have this rather unusual screwdriver you can break the tiny pins in the screws and unscrew them with a regular T8 or T9 Torx screwdriver. Seven screws need to be removed (yellow circles). One of them is hidden behind the white sticker with the barcode and not behind the black sticker where I looked for it first (red circle).