You'll probably want to get this achievement on missions "Uplift Reserve" or "Data Hive" (if Campaign, but FireFight also possible) since there are plenty of needlers and enough enemies to get this achievement.
As you probably already know, grunts are the easiest ones to kill. Try to focus on them, followed by the other covenants.
If fighting a brute, don't waste your needler ammo until it has lost its shield/armor (meaning, use another weapon). When you finally see the brute's ugly face, finish him with the needler.
Play those missions on easy if you like. This way, you'll do more damage and your health won't drop as much as on Heroic or Legendary.
Remember that if you get killed, you will return to last checkpoint and... last obtained needler kills.
You will get this easily, trust me!
PS: Some people seem to give a negative evaluation on this solution.
I really don't mind getting thumbs down, but at least have the decency of sharing "why-you-don't-agree" with other gamers!