The best way to get this achievement is by playing on The Ark. Get to the bit with the crashed Pelican there will be a Rocket Launcher. Once you have killed off the Brutes, two Prowlers will come your way, hopefully one of them will have three Brutes on it. Do not fire the Rocket Launcher straight away as it will only kill the Brutes but not the Prowler itself and will not count towards the achievement. Try shooting it with a smaller fire arm then finish it with the Rocket Launcher, that way the vehicle will be destroyed. An easier way is in the hanger of Crow's Nest. Two Phantoms come inside the hanger, three if playing on Heroic and Legendary. There are two turrets in the area, or you can run up and stick the turret with a plasma grenade (spike grenades aren't strong enough to blow the turret to pieces). You can also wait until after Forward Unto Dawn drops off the three Scorpions and the Gauss Warthog. There are multiple opportunities where a Phantom is stationary and in range. Using the Scorpian's primary weapon, roughly 5-7 direct hits will shoot it down. Another simple tactic would be to use a Spartan laser against a Prowler, of course with a well aimed shot.
Just looked it up real quick. Good Luck.
