At first of course select the challenge before starting - otherwise it won´t count!
As the game doesn´t explain too much you maybe asking "how do I mark an enemy"?
Well, the solution is, aim at an enemy with LT and THEN hit the A-Button. If done right, a skull will appear above the enemy´s head. Now your partner just has to kill the enemy - repeat this five times and the challenge is completed and your achievement should unlock.
Maybe interesting to know that not only humans count as enemies but also dangerous animals like wolves and bears. So it is possible to gain this achievement right after the beginning of a match by marking and killing five wolves.