On Easy, this achievement is fairly simple as long as you don't kill every single enemy or die. In the beginning section, you really only need to kill the elite. At the grav lift section, throw a grenade at the lift when there is only one enemy left so the next wave will come down on the grenade. The biggest time save in the whole level, however is the grenade jump that occurs in the hangar of the ship. It requires 2 plasma grenades and a frag and allows you to skip a major fight. Once you get to Keyes, make sure not to allow him to die because the whole section after saving him to the point where you kill camo elites is one checkpoint so if he dies during this time, you may lose anywhere from 40 seconds to over a minute per death.
I recorded two different easy speed runs under par time (20 minutes). One of them is done without the grenade jump (if you refuse to try the trick) and one of them with the grenade jump. If you are attempting this achievement on a difficulty above easy, especially on legendary, I highly recommend that you learn and use the grenade jump because it saves so much time. If you do not know how to do the grenade jump, watch my speed run with the grenade jump and skip to 9:20
. I jumped slightly too early so I didn't get as much air as I could have.
Without the grenade jump (18:18):
With the grenade jump (13:09):