(1) While this is the first "boss" level, its layout and execution are actually pretty simple in comparison with the other levels of the game. As soon as you open the entrance door, 2 facehuggers will attack. Kill them and move forward.
(2) You are now in a very large, rectangular chamber. You are standing on a curved walkway at the bottom of the chamber, and the queen is situated at a longer, similar walkway on the end opposite you. Branching off that far walkway is a short segment that extends to the queen herself, allowing you a way-cool look at her ovipositor. There are also 3 natural pillars within this room.
(3) The tactic is to zigzag left and right as you work your way forward, grabbing powerups and killing all the eggs and facehuggers encountered as you approach the queen. Be careful not to hit the queen in the process! She will stay attached to the long ovipositor until you either shoot her or have been in her immediate vicinity for a short while. It is best to take out as many eggs (especially) and facehuggers as you can before the queen becomes activated. Once she is chasing you, you tend to be less careful about activating eggs and releasing 'huggers! On HARD, the number of facehuggers revived and running around can be truly daunting if you aren't careful not to release any from the eggs.
(4) If you want to give the queen a more sporting chance and risk multiple facehuggings, you can dash around, turning to fire at the queen regularly until she has been put down. The safe (and, I think, reasonable) thing to do on HARD is to take refuge on 1 of the 2 walkways in the chamber and snipe at the queen from that position. She will NOT be able to damage you in your protected position--just keep your back to the walkway edge and the queen can't reach you! It's easiest just to shoot from the queen's walkway since that is the one you end up at, but both walkways provide a secure stand. The walkway extension going out to the queen's ovipositor is ideal (toast the egg first!); the only drawback is that it is very difficult to get onto it without prematurely picking up the pulse rifle magazine right at the junction. You will use up SEVERAL pulse rifle magazines (yes, this is the weapon to use here) before the queen expires.
(5) Once she is dead, the exit door opens. You can now finish off any remaining eggs and facehuggers in the level prior to exiting. There are 31 eggs and 6 facehuggers on this level. If you don't get 100% for ALIENS, try the level again, varying your pattern a little to catch all the enemies. Here is a quick rundown of the available powerups: on or near the entrance walkway are a shotshell, flamer canister, and med kit; directly behind the first pillar is a shotshell; and on or near the queen's walkway are a seismic charge, grenade, 2 med kits, pulse rifle magazine, and flame thrower fuel.