Just Cause 3

Didn't unlock for me either. I tried to press Start followed by "Reload last checkpoint", killed it again, and still no achievement right after killing it. Am restarting console now to see if it resolves the problem.
BTW, you should put the youtube video in your solution, so you have both text and visual solution.

EDIT: completely restarted console (not just shutting it down and restarting it, but a cold reboot). Had to do mission 2 (Taking Control) all over again, even died on the final boss level... but got the achievement. So... if you notice the achievement doesn't pop immediately after killing the boss, restart console and do the mission over again.

This needs to be flagged somehow so people know to watch out for it. It's nice that there's a note when you click into it, but there's nothing to let me know from the achievement list that I need to be worried about this one. It didn't pop for me and you cannot replay missions apparently. So I'll have to start a new game. And since there aren't multiple save slots I'll have to finish everything else first.

I was just looking up why this achievement wasn't popping for me and found a solution that may help. After the mission completes if you don't already have the achievement don't leave the boss arena and go up to the boss to shoot at it more until it does pop. Apparently it can "die" for the mission flag but not actually be killed. Hope this helps!