My phone was shutting itself off even when it showed higher than a 50% charge. This prompted me to use a battery-monitoring app and discover the battery capacity was less than a third of its original capacity. These two factors combined convinced me the battery needed replacing.
I followed the steps pretty much as they were written, though I used a heat gun instead of the iOpener to loosen the adhesive. The trickiest part for me was prying off the glass panel that covers the camera because there isn't much of a seam to get a knife into.
1) As long as the heat isn't too high, I'd say use plenty of it to loosen the adhesive—it makes prying things off much easier.
2) I used adhesive tape (https://www.amazon.com/dp/B00BXYWXY8) to stick the battery and the panels back on.
3) Plug the cables back in and test that the phone turns on before gluing or screwing anything.
4) I learned the hard way that the inside of the glass panel over the camera has a thin black coating that is easily scratched off, so I'd say when removing and applying adhesive to it, be careful not to scratch the coating. I switched from using a knife blade to a plastic tool.