Without the servers, AEGIS will stop attacking (the timer will stop) and can be entered for manual control.
Use a portal under the now removed window and one near the ceiling to the right of the turret dispenser to fling yourself with friendly turret to the last server room and destroy the remaining servers.
Use one to bring a friendly turret to destroy the servers here. It will explode, breaking glass and making it possible to open a portal upstairs.
Go upstairs and grab the 50's turret near the window.
Take care because a 50's turret will appear here, as well as on the second floor (those can harm you).
Enter the left room and use a turret from the dispenser on the far side of the room to destroy the servers on the bottom floor, like you just did in the previous room.
AEGIS will start draining oxygen, limiting you with 4 and 6 minutes in Advanced and Story mode respectively.
After destroying all of AEGIS' servers in the right room, return to the central room.
Should the turret die, another one will respawn in the dispenser.
A white turret will be in the dispenser.
Use portaling and jumping on furniture to avoid the electrified water, or use portals with the water flow to extinguish the fire and portal to the back. Proceed to the turret dispenser on the back.