To obtain this achievement you must run from beginning to end SOLO without doing anything but running and jumping, and you can use warthogs if you want.
Avoid the Hunters at all costs as they can send you flying across the map and might fall off a ledge. So RUN AROUND THEM.
P.S. I did it first attempt, its easier then it looks.
P.S.S A way to not worry about the elite at the end with the sword, you can put a warthog into the hallways before going down in the building, if marines are inside they can kill the elite with the sword and if you don't have marines you can always put it on its side to block the walkway so the sword elite cannot follow you (credit goes to Dannyework87 and NJDUKE)
I found a great and fast video done by Korbek gaming he does this in about 6-7 minutes. This will net you this achievement in a breeze.