This achievement is easier than it may appear. The main thing to remember is that the achievement still counts if you get it in a game with only one other person. So, try matchmaking in the small team game and small free for all playlists. Avoid peak times(evenings and weekends) to have the highest chance of getting a 1v1.
You may need to wait a while until someone actually turns up, but it should be worth it, as once you have a 1v1 the chances of getting the achievement are much higher.
If you get more people you can either make sure that they do actually get into the match, by waiting until the very last second of the countdown to quit matchmaking, or you could play anyway and just make sure that you know the name of the person you are trying to kill and avoid anyone else.
The only times you will run into trouble is if you keep on getting matched with lots of people, in which case leave it and come back another time. Or you get matched against a particularly good player, in which case try using weapons that may be considered 'noobish' like the dual-wielded shotguns, the stickygun, RPGs or miniguns.