I managed to snag the achievement by using some skulls and having the game on Heroic. I had the Battle Rifle and Plasma Pistol on me the entire mission.
Skulls:Catch
Famine
Fog
Iron
Masterblaster
That's Just... Wrong
Thunderstorm
I basically started the level out as normal and stayed in the beginning area killing everything until the Hunters showed up. As soon as they showed up I left and ran the rooftops avoiding everything until I reached Hotel Zanzibar. By this time I had roughly around 26k. After killing the enemies that were in the hallway, I rushed outside and ran for the Ghost and boosted past all of the enemies until I got to the tunnel. I hit the first load zone and went back to snag the Warthog and I proceeded to run through the level as normal. I mostly used this speedrun by Halo2Vista Guy as a guideline for the warthog run: