This will be the step where you teardown the controller not take it apart.
To remove the 4 buttons (2 on each side), first lift out the R1 (or L1) button. This may require you to wiggle the button.
From here, you will have to apply force to tear out the R2 (or L2) button and the plastic it is connected to. In the 2 pictures (ots) you can see one side taken apart and the other as it normally is.