This achievement must be accomplished in a ranked match. Player matches DO NOT count.
If you are boosting this achievement with one other player I found that it is best to do this on team elimination or elimination on training facility. Training facility is the best map, I have found, because it is small and all you need to do is climb up on the boxes and everyone is in plain sight. Set battle meter to 10,000. This allows for 13-14 consecutive kills before a winner is declared. After each kill the game will let you know how many kills you have in your current chain (streak).
This achievement will unlock after the round is over.