After being butchered at least a dozen times, I switched to the heavy rifle even though it usually isn't my weapon of choice. As soon as the cutscene finished, I ran like hell to the right and hacked the door. This gives you access to a ramp leading to the second floor. If I remember correctly it is a level 3 lock, so make sure you have that skill level (you'll need it later this level too). Sprint up the stairs, dropping some EMP or gas mines if you have any. At the top, you should see a code panel on the wall controlling the lasers. You can hack it (level 3) or you can search the locker in the ramp locker for the code.
Once you hack this panel, enough time should have passed that the boss will attack again. Use your heavy rifle and unload the full clip on her. This will stun her for a second, then she will charge again. As soon as she is about to launch her Typhoon, sprint to get out of the way. Unload another clip and she should temporarily retreat.
This will give you enough time to hack the security terminal in the center of the room (also level 3). Switch the turrets to enemy and then leave the computer. Now, all you have to do is wait for her to attack again. Eliza will give you the heads up, the boss will appear, and the turrets will utterly waste her. Personally, I was a little surprised at how hard it was to take her down on my own relative to how quickly the turrets took her down.
You can also use the power cells as outlined in the other answers, but I didn't have the dermal armor or leg upgrades (or skill) to survive such a strategy.