Note: Must be done on Heroic or legendary difficulty (Heroic recommended)
Using the video provided by Warzone guides, you can get the first wraith, (if you plasma the first wraith and the elite will get out, then just kill the gunner and jump in the wraith) and remove its wings on the sides to put it in the mammoth, getting it across the river.
Once you get to the next location where you must take down the shield there is 1 wraith there, make sure you finish the final blow killing the wraith with your wraith. I can not confirm if a marine gunner kills it that it doesn't count or does count so try to get the final blow.
After the shield is down, proceed to the next area, MAKE SURE to destroy the Gauss warthog, this took my achievement away my first attempt, then destroy the forerunner shit and kill all ghosts Wraith coming down, if done correctly you will have the achievement before you are supposed to go into the Covenant lift to destroy the ship.
This can be done in Co-op but you must take turns doing it 2 times because the Wraith kills only count for 1 person even if someone is in the gunner seat.
If you would like to kill 2 birds with 1 stone you can also do the par score achievement, which I also got from the same mission since you are killing so many enemies, just put the skulls CATCH, FAMINE, FOG, and TILT on, this will give you a massive multiplier. I finished the mission 2 times, a par score of 40k and 35k, just don't waste too much time after you obtain your achievement.
To save a ton of time when you get outside for the 2nd time towards the end where the giant scene is going on, you can skip the massive battle by grabbing a ghost, go around all the enemies following the right wall, right before the barrier use a jetpack to jump on the wall, run on top of the wall and over the barrier to finish the mission.