RedHedd said it best. Documentation is everything. See if you can get copies of the police visits to the premises. Make a recording of the noise and fighting going on (I'm assuming the landlord lives off the premises). When you've got all that together, sit down with your landlady and lay it on the line. Also find out about the noise ordinances in your area.

I signed a 12 month lease for a nice garden apartment. My landlord told me there was a woman with two kids living upstairs who were very quiet and that it "wouldn't be a problem as the kids go to bed early. The heck they do!! She never let them go outside to play, so needless to say I heard "ring around the rosey" constantly, not to mention everything else that went on in the apt, including her bf's puppy whining at 4 am. I called the cops when they started tying the dog out on the railing of the hallway.

After they moved out (it seemed like FOREVER) I moved upstairs. I will never again live below anyone.