The L1 and R1 buttons are held in by two clips. If only one clip releases, move your spudger to the other side of the button to release the remaining clip. Don't continue prying on one side after a clip is released, or you risk breaking the other clip.

Insert the flat end of a spudger in the gap between the L1 and L2 buttons.

The buttons tend to shoot out in the next step. You can place your thumb over the button to prevent this.

Use the spudger to pry out and remove the L1 button.

Repeat this process to remove the R1 button.