For this achievement you need to kill Argus. Argus only seems to appear in the Merciless Labyrinth and the hardest labyrinth (forget the name). His appearance is random and tied to the daily layout of the dungeon. Head to this site here :
https://www.poelab.com/15yt9/Under the today's layout tab you'll see an option for each difficulty. If you click on one it will show you the layout of the labyrinth, and will have an A on the area that Argus is in (i don't think he shows up in the normal or cruel so you won't see the A icon there). So head to the area the A is and look for Argus. When I found him it was behind a special door, the same kind that leads to the Izaro fights.
I was on my flameblast totem character when I found him. I used Vaal Skeletons for meatshields and let the totems do the work and it was pretty easy. Not sure how hard he is in actual combat but he didn't kill the skeletons very fast so perhaps he isn't too strong. That site also shows you the special conditions for getting keys from Izaro for the Treasure Hunter achievement, if you still need that one.