This component was far more stubborn than the screen connector when it came to removal. I opted for a smaller tool than the spudger (small flat-head) and managed to disconnect it after determining the best bit size for the job. Screwdriver is metal, obviously, so being gentle helps to avoid damaging anything.
One of the shoulder buttons fell out when I was doing this step, along with the piece holding it in place. They go back in just fine when reassembling but make sure that they are oriented properly, of course.
Using the tabs (I could really only see one) on the side of the retainer proved essential for me to remove it and release the cable. Unless that happened that cable retainer was not moving for me at all. It did come out once the tabs were pressed though they did prove somewhat uncooperative with clicking back into place once I had installed the new battery. Also, watch that the battery’s cable isn’t pinched when you’re putting everything back in place.
The iFixit info on the Vita battery product page stated to calibrate the battery before use. Not sure if that has to do with the complications you’re facing but worth considering.
Yeah, I’d seen warnings about that online. Apparently, when you install a new battery there is a surge of power as everything is reconnected. Removing any cards in any of the slots is advised to prevent damage to them.