BenjaminSJockeys: No, you do not need to kill 1000 loyalists, or 10,000 civilians in one session of running the game to set off the relevant achievement. The numbers ought to carry over between sessions (a single session when you launch the game, play it, and then quit out). However, the debug panel and console of the GOG version of the game does not seem to surface the totals in an obvious manner, and Galaxy does not appear to provide the ability to show a progress counter on this type of achievement either, but we'll see if there's some kind of solution.
Lastly, because you're new to the game (we hope you're enjoying it!), what you might not know is the following: the game is over five years old and was not originally designed with achievements in mind. Achievements were added on other storefronts only in the summer of 2017 and even then they were not 100% reliable (IIRC two achievements were permanently removed because of how unreliable they were). Getting achievements to work with the GOG version in 2021 was its own challenge, because the GOG Galaxy SDK and the process for getting achievements to function as intended is a different process to other storefronts.
I understand the situation with achievements, and appreciate your work a lot.
I'm fairly new to the game, yeah, but started playing a few weeks before the achievements were launched on Galaxy's version. Thus I had most of the campaign done, and did numerous runs since, more frequently with after every hotfix.
That's why the kill count achievements concern me: even without proper tracking for pre-achievements numbers, I should've gotten at least the faction specific ones long ago, I'd figure. But was able to get one only during a longer session, deliberately focusing on campaign missions and freelance contracts against one particular faction.
Anyway, thanks for your time, the game is awesome either way!