While all turrets and traps work for this achievement, you want to go for this achievement only if the enemy team has a Symmetra, because her little beam turrets are plentiful and are easily destroyed.
Once you find that the enemy team has a Symmetra, you're basically going to have to bully her for a while. Find out where she's setting up camp and keep running in there, taking out her beams, and running away. Don't worry about killing her, because that might turn her away from that location and you'd have to find her all over again.
Keep in mind that this has to be done in only one life. If you die, it resets. So keep dropping in, killing a couple turrets, and leaving to get some health and to let the Symmetra reset her beams.
And if you're playing with a friend, it might help to have an escort crew running with you to make sure you don't get too banged up or to keep you healed.