Make sure you have full ammo for either the laser chain gun or volt rifle (best weapons against her IMHO).

When I got to the top platform and I could see Petrova across the platform from the other side, I fired a shot at her which started the cutscene. Don't walk up to her because after the cutscene you only have like 2 secs to get away and usually you die because of the ammo of firepower thats fired at you at close range. As I said stand at the top of the platform across from where she is, then fire one shot at her... the cutscene will cue in and then after the cutscene run or jump from platform to platform all the way down to the bottom of the platform. Hide under the stairs at the bottom and wait for her. Or you can run into the tunnel and she won't follow you into the tunnel. Usually she will be the only one to follow you. Once you see her unleash all the ammo from either the laser chain gun or volt rifle. I used the laser chain gun... and I just unloaded clip after clip on her until she died. And I was lucky because after one clip was done, she was still stunned so i had time to reload without her firing at me... and before i knew it, she was dead.

I think I used about 300 rounds from the laser chain gun to kill her, but don't quote me on that.