I must have had a different model because there weren't any screw near the trigger on top of the battery for me. Those screws were located under the battery, which you can lift up (it is a little sticky). To do this on mine, I had to detach the rail from the lid in order to give myself enough clearance to lift the battery out.

Originally, I tried to do the next steps without lifting the battery compartment, but it was too difficult to mess with the locking mechanism on the ribbon.

Be careful when removing. What is not noted here, is that the SL, SR, and reconnect buttons will fall out. Just make sure you are over a table so they don't get lost.

My joycon would not open as cleanly as what is pictured here. The white box at the bottom of the controller in the last picture stuck to the top compartment and became detached from the part with the battery. It's possible it could have detached the other way, but I didn't risk it. I was still able to do the repair, but it gave a much tighter window as I needed to be very careful to not be to forceful on the battery wires.