My nine-year-old Vita still worked, but its original battery was not in the best condition. I obtained a replacement battery from iFixit and used this guide to install it. It may look daunting at first, but if you study the guide, take your time, and follow the steps carefully, it’s actually pretty straightforward. Having a spudger definitely helps.
When reinstalling the battery retaining bar, be sure to insert the bottom end (as shown in the photo) into the slot before driving in the screws. If you just lay it on top, you will crack the bar.