Turrets are stationary objects with machine guns. They have a light that shows it's field of vision. The light turns red if it spots you and will start shooting at you.
Destroy turrets by damaging them with weapons, plasmids, or a combination of both. This can be unlocked easily just playing through the game if you find and destroy most of the turrets.
If for some reason you're having trouble, or missed it on a previous playthrough, you can reload the same checkpoint and destroy the same turret over and over and it will still count towards the achievement.