My 820 has needed a battery for some time now so I just replaced it with a EN-EL10 battery from a Nikon camera. I just happened to have one on hand. The dimensions are identical and it is super easy solder because the onboard battery charge controller has exposed pads to solder to without overheating the battery. The original battery also has an onboard battery charge controller which I did not swap. I just soldered power wires directly to the battery and the battery charges just fine. After replacement, from a 100% charge and recording an activity for 2 hr with the backlight at 30% the whole time, the battery level is at 83%. Best of all is that the after market EN-EL10 batteries can be had for under $10 from Amazon with advertised higher rated capacity. Mine was a Promaster branded battery rated at 800mAh. There are some that are rated at 1400mAH but who knows if that is true. It can't be as bad as the one it is replacing. I had nothing to lose as the 820 is super old and obviously out of warranty. I used a 3D printer with a heated bed set at around 70C to soften the adhesive on the screen evenly by placing the screen directly on the bed. When the screen is heated sufficiently, a stiff thin piece of mylar packaging material (like from a package of dehydrated camping meal packs) was insert between the bezel and the screen, slicing the adhesive back and forth and gently pushing deeper as it went. I did not go deeper than about 3mm to prevent damaging the two connector ribbons. Once one side was sliced, I went all the way around to release the screen without prying. It is not as bad as it sounds and is pretty easy. I used limonene to clean off the residual adhesive from frame and display so that I could apply new adhesive display tape and reseal the unit like the factory to keep it water tight. It's now been a little over 2.5 hrs and it is reading 76%. The battery wires were soldered to the new one without any stripping and there is just enough wire to reinstall the battery to reach the board. The display tape was used to secure the battery.
Disclaimer! Proceed at your own risk if you are going to do this yourself! This post is meant to share my personal experience with the process and results. Hopes this helps some people. Happy new year!