I did this on a solo run, Heroic. Apparently there’s some glitch if you try do this on co-op. The achievement doesn’t pop for everyone. They’re tips that you should use a combo of either the rocket launcher/fuel rod cannon and a precision weapon like carbine/battle riffle. I found unloading the rocket launcher into the phantom works just fine. But I think the trick is ‘sneaking’ up on it. Credit to LifeExpectancy for that tip in the walkthrough.
Follow the video for the exact location of the launcher. Either way, this is the area where there’s a phantom wreckage and a fight with the covenant. Stick to the right and climb up the ledge and about halfway up will be another ledge. Climb this and you should find the rocket launcher with a rail gun. Now continue up the ledge, sticking to the right and sneak up till you can just about see the phantom between the cliffs and get a lock-on with the rocket launcher. Get both shots in and immediately reload. You should have enough time to get a lock-on and empty your last shots before the phantom takes off. The last shot should do it and achievement should pop.
Let me know if this doesn’t work for you, or anything more I should add on. Cheers!