Have your XCOM Squad go from 100 health to 0 in a single AI turn.
You need to allow your XCOM Squad to be killed in a single AI turn. There's a cheap strategy, though it may be a bug in achievement. It seems game doesn't really check if damage occured on AI or your turn, so to get this achivement you may simply start a game in atomic/information era, move an XCOM squad away from your cities and drop two nukes next to it. This should be enough to kill it, at least that's how I got this achivement.