My fiance is on a K1 and was arrested for a misdemeanor(battery) against me. We didn't start the AOS process and the court date is after expiration.

Are you still within the 90-day period? If so, you should start the AOS process immediately. If not, you still need to start the AOS process immediately but it will be different as you will need to file Form I-130. Whether she will be able to ultimately become a resident will depend upon the outcome of the criminal case. I strongly encourage you to work with an experienced immigration attorney. You can read more about the AOS process at http://myattorneyusa.com/family-immigration.