It didn't have any achievements at launch, but the recent update has added them. I saw the Tough Guy one come up after punching 5 enemies out in Winslow Bank. Unfortunately, I didn't get Treasure Found which comes up when you find your first collectable. It's listed in my ingame achievements list, but not on the "My progress" page in GOG Galaxy. Must be because I found the first collectable BEFORE the update.
I also have played the PS4 version, and the difficulty specific achievements (one for Sleep Walk, one for Field Agent, and one for I want XIII) don't seem to stack, at least on that one. So if you finish on I want XIII, you don't get credit for the lower ones. The 3rd difficulty, Super Agent, gives you no achievement.