(1) This is definitely one of the tougher levels to figure out with all of the sequenced lifts involved. There are also a large number of company soldiers here, as in the last level. It is most convenient to simply grenade (or seismic charge) them all into oblivion. Even though there is only 1 grenade powerup (=5 grenades) on this level, there are lots of grenades available in the next level, and if you don't miss much you will still come out pretty well stocked up.
(2) Start by moving straight down the hallway you begin at to a junction. There are 4 soldiers here; kill them with grenades or seismics. (While near this junction, you may occasionally have a facehugger from the area below you jump up onto the railing or walkway and come after you!)
(3) Turn left and move straight ahead across an open walkway and across a lift platform to a stairway inside a corridor. Kill the soldier that comes up the stairs after you. As soon as you touch the med kit at the bottom of the stairs, 2 doors on either side open, each releasing 2 facehuggers. Kill the 4 'huggers and move forward (there is another med kit behind the right-hand door if you need it). Blow the crates just ahead to get the battery. Keep going until you reach a second stack of crates. These hold 3 facehuggers, 3 derm patches, and the auto-map. There are also 3 more 'huggers lurking behind the crates. Be very careful not to get facehugged in the narrow confines of the hallway.
(4) Having cleared your way, move forward to the switch and activate it. This powers up the lift platform back at the end of this corridor. Now backtrack to the lift, killing 3 newly-materialize soldiers and any revived enemies on the way.
(5) Walk onto the lift to make it rise, and step off it to the RIGHT when it reaches the top. Kill the company soldier here and WAIT for the (now-unoccupied) lift to go back down before proceeding.
(6) Move away from the lift and to a doorway. Opening it unleashes 4 'huggers--kill them, then flip the switch inside. This raises the lift back up; if the lift was not all the way down yet, you are stuck and will have to make a 5-point fall to get back down (sorry--armor's no help here!).
(7) Now move off the lift (you may be battling some revived enemies as you do so) and go straight through the junction mentioned earlier (the one with the 4 soldiers in it) dead ahead to a lift similar to the one you just came down on. Go across it into another corridor and stairway. Touch the derm patch below and 2 doors open, releasing a pair of soldiers (one to your left and a second around the bend just in front of you). Dispatch them and grab the med kit in the room around the bend if you need it. Now move down the unexplored hallway (to your right as you entered this area) until you reach a pile of crates. Each of these 4 crates holds a 'hugger, with 3 more of the critters waiting on the other side. Beware of multiple 'huggings as you deal with this group
(8) Now activate the switch ahead and do an about-face, heading back the way you came. There will be 1 freshly-materialized soldier on your way out in addition to any "revivors." [BUG! Before proceeding, I recommend reversing your route and re-killing all the now-revived facehuggers at the other end of this corridor. The reason for this is that a sequence-related glitch in the coding prevents you from achieving 100% for ALIENS at the MISSION ASSESSMENT screen, even when ALL the aliens in the level are actually killed, simply because the level is played in this particular order. This is probably the most convenient location in the level for topping out your score. On the other 2 difficulty settings, explore alternate routes to find the "correct" sequence.]
(9) Kill all the enemies and step onto the lift to raise it. Get off to your LEFT at the top and kill the 2 soldiers. Once again, WAIT for the lift to go all the way down before proceeding away from it to a door.
(10) Open up and kill the lone soldier within before flipping the switch. This re-raises the lift you just came up on and opens the exit doorway.
(11) Go back to the lift and walk onto it and it will drop down after a few seconds; a company soldier makes a fresh appearance at the bottom. (Again, if you activated the switch in the room prematurely, the lift stays down and you will lose some health points making the painful drop back down.) You may have to re-kill some revived enemies at this point. Now walk off the lift (with the corridor and stairway at your back) and take an immediate right down the open walkway. Walk onto the elevator platform under a gantry to go down.
(12) Blocking your exit from the elevator at the bottom will be a row of crates. Two crates house 'huggers; the best way to deal with them is to shoot a gap--2 crates--in the left end of the row (yielding a derm patch) and move out into the courtyard area. Now you can deal with the remaining crates and the 2 facehuggers from afar (don't worry--you'll receive 2 more derm patches for your trouble). You are ready to activate the switch (which enables the elevator) and blow the remaining crates in the area. The crates will yield a grenade, body armor, and a hypo pack. Grab the hypo pack last and make a beeline back up the elevator.
(13) Kill the new soldier at the top and head full speed to the lift platform that was up the stairs from the derm patch (this would be to your right as you ran back onto the elevator to go up and is in the opposite direction as the soldier you just killed). Run onto the lift and get off to your LEFT at the top. Another newly-appeared soldier will be there to greet you.
(14) Dash ahead onto a new lift platform between 2 switches and it will go down, but try to kill the soldier here first. (These 2 switches, by the way, will re-raise both the other lift platforms if you happen to get stranded by one of these lifts and are lucky enough to be on this section of the walkway when it happens.)
(15) Beware when you hit bottom as your hypo pack has most likely run out. You are standing at the top of a stairway; 4 facehuggers and the exit doorway are below. Be especially careful not to get facehugged in the very narrow confines here; this is especially annoying when it happens so close to the exit door (believe me).
(16) Be sure to grab all 3 derm patches on the stairway before making good your exit.