What I did was kill all her Black Hand escorts first, before I tried to engage her. To do that, jump around a lot, take cover in the rooms near her and also around the ramps (go down, etc. -- usually you'll only have a few following you at a time instead of the whole bunch).Once you get rid of the other enemies in the room, the Volt Auto Rifle works very well on Petrova. It keeps her stunned (except when you reload), so she hardly does damage to you.
You can find the Volt Auto Rifle in the previous level inside the alien UFO. If you missed that, go explore this level some more... there are a lot of them in the sleeping quarters or whatever they are (the series of rooms with beds, Nod posters, bookshelves, etc.).