OK, I did some testing and managed to find the achievement storage for ELEX. They are stored within two files called "UserDataA.bin" and "UserDataP.bin". They are located in "%LocalAppData%\ELEX\Config".
Steam version doesn't use or even create these files, whereas the GOG version creates them upon launch and edits them every time you unlock an achievement. Thank you "Up and Away" achievement, you made it very easy to research this lol.
Now GOG galaxy seems to sync the entire "%LocalAppData%\ELEX\Config" folder which is nice, but it's still good to know where these are stored for manual backup for people who prefer offline installers to Galaxy.
I was really sceptical about these being stored within the save file and it turns out I was right. The only game that I'm aware of, that stores Achievements within the save file is Deus Ex Human Revolution. You can literally load another person's savegame and watch like 50 achievements pop up at once.
I would propose that the Spreadsheet should be updated with a new column with information on where these in-game achievements are actually stored, since, in my opinion, if someone bothers achieving them, they should be able to back them up easily.
Excellent deductions, I myself have observed that some games store in-game achievements information in separate files, and in many cases even PCGamingWiki doesn't seem to have this information.
For some games I haven't yet been able to find the path. If Marko thinks it would be useful I could post what I know about some games, and together we could try to get to the bottom of the unsolved cases.