Along with getting a kill with a breaching charge, this has to be the biggest pain in the neck to get.
Most skilled players will destroy your barbed wire so I highly recommend you play Casual mode for this as a lot more "nooby" players will be playing.
You need to be defending the objective in order to get this. Take notice of where the objective is and try stray away from it but don't go too far because if you are miles away, chances are, the opposing players won't come that way to the objective. Try camp a popular route and make sure you are in a spot that is particularly difficult for the enemies to see you, because you want them to think they're safe, that there's nobody at all around. Wait for them to start trudging through the barbed wire at a snail's pace and just mow them down with your weapon of choice.
EDIT: Thanks to TFV Ghost for this info. You will need to get a straight kill on the player whilst they're in the barbed wire. The achievement won't count if you put the enemy player into the revive state before killing him/her.