This will prevent it from firing at you, so step through the first portal and - quickly - pick up the turret in front of you, before dropping it down on its side. As you turn the corner, look for the wall-mounted camera and fire the exit portal so it expands the bridge right across the room. This will protect you from the four turrets located around the corner to your right.
Walk into the jump plate and the light bridge will stop you, allowing you to run across the transparent glass. Drop down into the centre of the turrets (right on top of the Companion Cube) and then pick up each turret in turn (or knock them all over however you see fit).
As you look towards the exit, set the exit portal directly in front of the two turrets blocking the exit. Now run up right beside them (to the side) and place the portal up above. This'll allow you to run past the turrets and into the exit elevator.