At the end of the second mission as a Marine, you'll find the Alien Queen. The battle takes place in 3 phases:
In the first phase, simply defend yourself from facehuggers while you wait for the furnace to power up. There are flamethrowers and grenade ammo lying about the room. Use the grenades to blow up eggs before they hatch and pick off any facehuggers with the rifle; flamethrowers are efficient in taking out eggs but not the facehuggers themselves.
After the furnace powers up, use it and it'll take away a third of the Queen's health. If you're quick you can shoot grenades straight into the glowing canister either side of the Queen and take away another third, much quicker than shooting the canisters.
Now you'll have to defend yourself from aliens while you wait for the furnace to power up again. Remember to keep your health high, as getting grabbed at low health means instant death. There are stims located on the floor to the left of the Queen. Dash for the furnace when it's powered up again, the cutscene will play and you'll get the achievement.