This is missable and requires actions from Act 1 or 2 into Act 3, so most of the game.
You have to go into the cellar (located in the kitchen) of the abbey during Act 1 or 2, if you go all the way to the left, there will be cats with some sausage, and you'll get a cutscene where you feed them. The cutscene is the trigger, if you don't get the cutscene it didn't work correctly.
In Act 3, there will be a section where you get to go into the abbey again (it's normally unreachable during Act 3) and there will be a an area where you run into cats, with another cutscene. You can't miss the cats, so if you don't see them then you never gave them sausage in Act 1 or 2.
After that you will go home and sleep, the next day you get to go explore it will have heavy snow on the ground, go to the inn (located in the meadows) and talk to Wojslav (he's cutting fish). When you talk to him you will talk about cats and the achievement will pop.
Notes:
If you're trying to do it in Act 1, do it before the murder, after that the cellar will be locked and even if you convince the person guarding it (also Wojslav coincidentally) a different cutscene will happen because of story. If you miss your Act 1 window though, don't worry, you can do it in Act 2.
There was previously a guide here I followed, it got deleted for some reason, but I was able to finish it through memory. They mentioned you could only feed the cats sausage in Act 1, but I forgot, and was able to do it in Act 2 and the achievement popped for me. I didn't pet any cats the whole playthrough, that doesn't trigger it at all.
I did end Act 1 in the abbey's favor, so in Act 2 I stayed in their guest house, unsure of if that affects whether the cats show up in Act 2 or not, just a thought.