I just successfully completed this repair on my LTE iPad Air 2. This guide is specific to the WiFi version, so there were some steps which were missing (but supplemented by comments from other people).

I ended up following the directions for removing the screen, then I followed the instructions until I reached the point where the logic board needed to be removed. At this point, it looked like there might be some differences between the LTE and WiFi versions, so I decided that I would not loosen the logic board from the top, but instead loosen it from the bottom. You just need to be careful not to put too much stress on the logic board when lifting it up. This way, I was able to pull up the logic board far enough to unhook and remove the battery contacts without the need to possibly damage some LTE connections at the top end of the logic board.

Once I installed the new battery, I reversed through the steps that I had taken. So far, it appears to have worked successfully.