Take a Hike
After clearing the first group of Covenant, climb the rocks on the right and turn around to enter a long alcove with a dead Marine and a Mission Intel data pad. In this alcove lie a Railgun and Rocket Launcher. Grab both of them before heading for the second group of Covenant where a Phantom will appear. When the Phantom appears, pound away at it with the Rocket Launcher and Railgun, making sure that the rockets lock on to the Phantom. Four rockets and two or three Railgun blasts are enough to destroy the Phantom.
While possible on solo, it is easier on co-op, as there will be more than one player attacking the Phantom. One player should be armed with the Rocket Launcher, while the other should use the Railgun. Having one of the players play as Kelly-087 makes this achievement even easier as Kelly's base attributes allow her to reload more quickly. In all cases, though, watch out for nearby Covenant, especially Grunts with Fuel Rod Cannons and Jackal Snipers.