If you are the spouse of an abusive US citizen or green card holder you do not need to stay with them. In this type of case you can self-petition and receive a lawful status for yourself and children if you have any. To qualify, you must show:
you entered into a bona fide marriage with a US citizen or LPR; and
the two of you resided together; and
you are a person of good moral character.
Generally you can show you entered into a bona fide marriage with a US citizen or LPR by providing a copy of the marriage certificate and proof of citizenship or Lawful Residence for your spouse. If you do not have this proof do not worry most attorneys can obtain it.
To show you resided together you will need evidence such as mail at the same address, joint checking accounts, or affidavits from witnesses.
The abuse can be show with affidavits from witnesses, pictures, police reports, a psychological evaluation and anything else that shows abuse. Moreover, the abuse need not be physical. It can be emotional, sexual, and/or financial.
Good Moral Character can be shown with affidavits and police clearances from your local sheriff's office.
It is also important to note that a VAWA application must be filed 2 years after a divorce. If you are not divorced you can file at any time. In certain cases it can overcome bars such as entering without inspection.
In sum, if you are in an abusive relationship you do not need to suffer to get your residence. You should speak to an attorney to see if you have a case to self petition.