Near the end of the level, you'll reach a section where there is a large highway with a small patch of grass in between. You will have to complete this section without damaging any civilian cars.
Use your shotgun, that you spawned with at the beginning of the level, and dash across the first part of the highway, onto the patch of grass where the blue car with enemies stopped. Make sure you shoot PARALLEL to the highway and kill these enemies (or melee them). That way no matter what happens, none of your bullets will accidentally hit any cars. After killing these 5 enemies, you will have to sprint and dash across the second part of the highway. Again, repeat the method above. Use your shotgun, and aim away from the road. There will be about 6 enemies and 2 dogs to kill in this part. After you eliminate the enemies, your teammate will rejoin you, and talk for 30 seconds before you begins to cut the fence. The achievement will unlock at that point.
If you die, it will reload the last checkpoint and you can still get the achievement.