simple battery is usually not a crime involving moral turpitude, so naturalization may be possible within the 5 year period to establish good moral character. We still need to know the facts of the case and review the criminal records to say with any certainty how the USCIS would view the situation.
Scott D. Pollock
The "petty offense" exception only applies to charges of inadmissibility. It is inapplicable in the naturalization context. That being said, simple battery is generally not considered to be a crime involving moral turpitude. Notwithstanding, the issue for you will be whether you can establish good moral character during the requisite period. Any time a criminal matter is involved with an application for naturalization it is best to be represented by counsel.
Before a lawyer could quote you a fee he would need to review the specific facts of your case. I have handled many cases like this over the years. Feel free to call my office at (561) 478-5353 to schedule a telephone consultation if you wish.