(1) This level is significantly larger than the last lair. You enter at the base of a large square area with 4 equally-spaced pillars; the queen is in a rectangular area ahead and to your right jutting out from the main square. Use a zigzag pattern and work the area methodically to cover all the enemies and powerups. It also seems best to kill enemies and grab pickups when you see them, even if you have to deviate from your intended route somewhat in order to do so. As soon as you open the entrance door 2 facehuggers perform an assault. Your only hope to escape without damage is to instantly exit the entrance room and deal with them in the open where you have room to back up.
(2) The most efficient way to proceed now will be to explore the area around the 2 pillars to your left first. In the "lower left" corner of this square area (as viewed on the map) are a med kit and flamer fuel if you need either. Now move forward, zigzagging as you explore the 2 left pillars. There is a pulse rifle magazine ahead, so I suggest using this weapon until you reach it. Methodically kill all the 'huggers and eggs. By the second pillar lie 2 derm patches.
(3) When you hit the far wall, work your way along it. Two derm patches, the pulse rifle magazine (don't grab it just yet!), a med kit, and flamer canister will be found here.
(4) Now stay left and explore to the left of the queen (your left--not hers), being careful not to prematurely disturb her by getting too close or hitting her with stray weapons fire. En route you will encounter a derm patch, med kit, adrenaline burst, and grenade.
(5) Retrace your route back to the pulse rifle magazine and grab it.
(6) Now explore the 2 remaining pillars, heading back toward the wall the entrance door is in. Switch to the shotgun here since most of the remaining ammo ahead is for this weapon. Don't miss the 2 patches by the first pillar and another patch plus a flamer canister by the second.
(7) In the "lower right" corner of the square is a shotgun. Grab it and turn around. Now move ahead along the wall. You will reach a corner with 2 eggs. Toast them and make sure you get the egg and derm patch ahead of you out in the open (approximately halfway between the queen and the "upper right" pillar).
(8) Now enter the area to the right of the queen. Along the right wall are 4 shotshells, and in the exit alcove (ahead and to your right) lies a med kit guarded by a trio of eggs and 2 'huggers. Near the pillar by the queen are a smartgun magazine, grenade, and pulse rifle magazine--don't even try to get these yet! Be very careful shooting the egg right near the queen or you may hit her. Also try to shoot any facehuggers near the exit area so that you will not have to walk over them in order to exit.
(9) With all the other enemies dead, you are now ready for the queen. Prepare to back into the exit alcove and shoot at the queen. She is not a particularly hard target so I recommend using just enough grenades so that, with the 2 grenade powerups (=10 grenades) available on this level you still can exit with 20 grenades total (assuming you had more than 10 grenades stocked up from previous levels). Shoot her once or twice to cause her to detach from the ovipositor and back rapidly into the exit alcove. The queen cannot reach you in here, so take your time and make sure of your shots. First launch as many grenades as you have decided to use and then switch to the smartgun. Keep in mind that there is 1 smartgun magazine available after you kill the queen, and that the "rounding trick" is in effect: if you have 800 bullets left the powerup knocks you up to 900, but if you have 801 bullets left it rounds your counter up to 999! At the appropriate time, if the queen is still alive, switch to the pulse rifle and finish her. For both weapons, INDIVIDUAL bursts rather than full auto (just holding the fire button down) seem more effective. Once the queen dies, the exit door opens.
(10) Run out to grab the powerups by the queen and make your exit, watching for any revived facehuggers.