This is a lot easier of an achievement than it would originally seem. There are multiple skips/drops that you can utilize throughout the level allowing you to avoid 90% of the enemies.
The achievement is not difficulty specific so I would HIGHLY
recommend doing this on easy, although using the method I did in the video below you could complete it on normal, but this would give you very little room for error and you must get lucky with how the enemy acts.
You can pretty easily get this along with the Hit the Beach achievement
part of this achievement will be the sword elite at the end. There is a way to trap him in the room if you park your warthog correctly (I attempted it in the video but did not get it properly) - basically you want to back up the warthog and block about half the door so that you have just enough room to jump through. I tested this multiple times and every time I parked correctly the elite could not follow me out. However this is unnecessary, it does make the end a bit easier if you get it right