This requires you to not use any weapons at all which includes any held weapons, the ghost's blue bullets and the warthog's horn. It is ok to use the ghost's boost or warthog's powerslide!
As you spawn, head up the narrow walkway towards the flipped warthog! Get inside, watch out for the choppers, and head for the entrance to the next area. Dodge the 2 wraiths and other enemies along the way. After getting past the 2nd wraith, you'll want to switch into the ghost that is sitting on a rock before the tunnel entrance. Feel free to also pick up the health kit if necessary.
Now you'll just be using the ghost to boost by enemies and avoid as much fire as possible. Just boost your way through the entire level and keep your eye on choppers as they will cause you the most damage. When finding a new ghost, feel free to switch to it, and always pick up health kits if you aren't at 100% health before entering a new area.
It is totally ok if you die for this achievement, and restart at your previous checkpoint. You can take your time learning enemy patterns if you need to.
If you follow this exact method, you can also unlock the following achievements at the same time: