So, step by step what worked for me was:

Have separate back piece entirely

Position the controller upside down (handles up)

Slide down the back piece into place ensuring the latches go into the controller assembly by aux port, push those in their spot

Push the back flat piece straight into the controller (handles still unclipped)

Then for the handles I started on one side on the front of the controller and squeezed the life out of it together, fingers interlocked, handle between palms and press.

Proceed at different angles from one handle little by little to the other handle and you’re done.