Whilst one of the other solutions (Mecha Werner) is good, I believe it leaves out some vital strategic ways to get this achievement, and instead tells you how to make the game forget deaths.
First off, I highly recommend doing this in co-op, as this spreads out the flood to both players and actually means both players fight LESS flood enemies by themselves than they would if you play solo.
First off, BOTH players need to not die. You can't pop the achievement for either player if one of the players dies, and one does not.
Second, use the 'Bandanna' skull (also notice in game that the the Bandanna skull is spelt incorrectly - it should be spelt 'Bandana'). The Bandanna skull gives you infinite ammo AND grenades.
Load up the level on Heroic (or Legendary, if you prefer). Near the start, in the first few sets of enemies, you'll have a couple of humanoid-flood enemies carrying shotguns. Other enemies will be carrying plasma pistols. These are the two weapons you want to use as you're going through the level, so pick those up as soon as you can.
Also, be aware of the large, exploding flood enemies, which I call the "Walking Wombded" (Walking wounded... wombs make more of them... Clever, huh?) enemies. These are the enemies that explode when you shoot or get near them, and release lots of the smallest flood enemies which can reanimate dead larger flood enemies.
For the smallest flood enemies, I recommend using the plasma pistol to get rid of them when you're at your feet, and shotguns for 'group' shots when they're in front of you.
Now, you want to take your time on this... you don't need to go for par time on this mission, so take your time, let EVERYTHING in an area spawn, kill it, and then move on. There is no place in this level where enemies infinitely spawn. You need to do this so you're not attacked from behind and in front at the same time.
In the areas where flood enemies jump out of the ducts (in the long corridors, where the ducts are up on the walls), they will spawn multiple times, and you'll need to kill them. However, with infinite ammo, this is EASY. As soon as you see them spawn (use your radar), start throwing grenades and sticky grenades into the ducts, ready for them to explode as they spawn inside. Back up as well, so that you aren't sandwiched between two spawn points. You ALWAYS want to have the flood spawning in front of you. However, there are a couple of bits (where you're waiting for Guilty Spark to open the doors) where you will get sandwiched. In this case, you need to have one of you facing behind you, and one of you facing ahead of you.
Furthermore, when you come to these 'waiting' segments, there may be rocket launcher-carrying flood enemies. In this case, try and grenade them with grenade-spam before they get off a shot. This is really your only choice for them when you've got shotgun+plasma pistol, and unless you fall down a hole in the middle of the path (watch out for these, as some of the flood can spawn up through these holes, and you really don't wanna do something as stupid as falling in a hole on this level!), the rocket-launcher enemies are your ONLY major threat in the level.
Also in the level, you'll be going through small thin hallways under the floor. There will be a lot of Walking Wombded enemies around the corners which can kill you if you don't get them quick. To avoid being killed by these 'jump-scare' enemies, Throw frag grenades (NOT sticky grenades) against the far wall of these hallways, near the corners, and let them bounce around the corner to kill any potentially-waiting enemy.
Continue slowly making your way forward, until you've gone up three large elevators. Take care to NOT fall down the edges of them, and you will eventually get to the end.
Hopefully, if you follow this advice, you should have no problems.
I hope this helps :)