As usual a while after the warranty had passed, my wife's Fitbit Alta HR stopped showing the heart rate and the battery life had dropped from 7 days to about one day. Basically it was no longer functional, and considering the cost of a new one being $133, what did I have to lose by trying to fit a replacement battery myself for $10 from AliExpress.
I watched the video at https://youtu.be/aE_8u2wtIOI and it was only about a 30 minute job. For this one the only real tool you need is the tiny Torx screwdriver. I had invested in a iFixit toolkit a while back so I had everything I needed.
The soldering of the battery wires was the most finicky part, and it is worth noting carefully how the wires are threaded down past the board. I had to reposition the wires after soldering the first time as I realised they would short against the two metal lugs under which the board must slot in. There are two tiny grooves cut into the board and the wires can pass down through there. I take photos too as I'm working so that I can reference back on something I may have missed, like this.
And that was it! Charged it for about two hours and it has powered up fine with all it's sensors reading.