She is always found guarding a Plasma Cannon, although it is not strictly necessary to kill her in order to take it.
As for many bosses, killing the Alien Queen unlocks a Deathmatch Arena.
The Alien Queen is fully immobile, relying completely on her psychic powers, automated defences and smaller minions to defend her.
She attacks by placing a targeting reticle over the Spelunker, which appears whenever the Spelunker comes within its very long range.
It will zap the location it indicates after a short delay, which will do ten points of damage and stun the Spelunker if they are hit.
As the reticle does not move once it has been placed, the Alien Queen's attacks can be avoided simply by moving out of the way, and not standing in any one spot for too long.
She has twenty hit points, and thus the fastest ways of killing her are with five Shotgun blasts, two Bombs, or the Plasma Cannon. The Freeze Ray will kill her instantly if you can damage her while she is frozen.
Alternatively, the Teleporter is effective when used offensively against the Alien Queen, as being telefragged will kill her instantly - but you have to be careful or you may teleport into the wall near her, killing yourself instead.
Another trick is to use the Spike Shoes by jumping between her and the ceiling, which is a one block gap most times. Keep moving to avoid her targets and she'll die fast.