You have a portal gun. So you can make two portals. In the main room a turret shoots at you, but it's quite slow...so you can shoot a portal in front of GLaDOS and a portal behind you, wait a few seconds and quickly walk away...then the turret shoots into the portal at GLaDOS everytime you do that a core falls off GLaDOS and you neeed to throw that core into a fire-hole-android-hell-thing and if you do that a few times Aperture explodes within GLaDOS but somehow you survive....
That's how you kill her in the first game.