For this achievement you must finish the mission flawlessly without any deaths. Make sure you have most of your upgrades unlocked in the armory (Extra health, ammo, grenades, etc.) I would suggest using the LMG which is the last weapon that you're able to unlock.
The most difficult part during the mission is near the end where you will need to jump on the turret. There will be enemies coming from your left, middle, and right. There will also be two health pick-ups on your right and left.
Make sure you don't shoot the health pick-ups until after most of your health is already diminished. ONLY start to pick them up when your health is almost gone.