After a round ends, win or lose, the screen goes into black and white with slow-mo for a moment and you are still able to act. The achievement is asking that you kill a player during this slow-mo time period. The only time it will not
do this is if the game ended with the conclusion of that round; in that case the game will just end.
If you are in the process of killing someone as the round is about to end, it's a good idea to wait until the round has actually ended to finish the kill. I will also say that you're more likely to get this when you have won the round as opposed to lost the round, since your team will have the upper hand. If you're with friends, you can try to coordinate to let each other get a kill, otherwise you'll have to look around trying to spot someone weak. Naturally this is easier to get with damage-dealers (flank class, damage class) as opposed to supports.
Here is a clip of when I got it (award pops up in the top left) if you're more of a visual person. You can also see what it means by "after the round":