I'm self-answering this because I know of a few actions which do count. I don't believe this to be a complete list though, so I'm definitely looking for other actions which I'm missing here:
- Doing the things on the list
The obvious one; killing people, animals, creatures, robots, synths, turrets and legendary enemies along with performing critical strikes, sneak attacks and backstabs will all increase their respective counter.
- Damaging things then having them die from other causes
If you attack something but don't outright kill it, but then it goes on to die anyway from other causes, it will increase the relevant counter. I guess you could say that you did contribute to the thing's death though, I suppose.
- Having your companion perform the above actions
If your companion outright kills things, or attacks things which die from other causes, it also increases the relevant counter.
- Using the Turret Override Program to disarm turrets
Disarming turrets counts towards the Turrets Killed listing.
- General game glitches
Unfortunately sometimes the game seems to increase these counters even when you've done nothing wrong. Not much can be done to avoid this other than keeping an eye on the counters and reverting to an older save if it happens.
Are there any others?
NPCs which are not your Companions who go on to kill things do not appear to increase any of these counters; neither do enemies which kill other enemies (even if they were ordered to do so by you).
