Right after the cutscene jump to the right and go on the construction bit where there is a ramp and the on to another higher bit so she cannot run you over.
There is a nail gun on the ledge so I advise you get that, also I suggest you already have guns, a few pistols do the job.
With your gun keep aim at her and when she stops to shoot you get as many shots at her as possible.
Keep doing this and she will eventually die.
If she drives away don't go where she is, go to the shop with swords in it and get some katanas to throw at her, when you come out of the shop run for the construction bit and she comes back.
Just keep shooting her and throwing things at her, son she will die.