Unfortunately, if a prosecutor declines prosecution, there is nothing that you are able to do about it. There is no appeal process. The DA has complete discretion to determine which cases to prosecute and which not to. They do not take on every offense reported to them, and even the President of the United States cannot force a prosecutor to go forward with a case if the prosecutor does not wish to proceed.
Cross-complaints (which is what you would have liked to see) occur when the police come to the scene of an incident and cannot determine which of two is more culpable, so they arrest both. If the police believe they have probable cause
to arrest only one of the two, that's all they will do. That's certainly what they will do if the police don't witness any part of the incident but a credible-sounding complainant comes forward to file a complaint. First to the police gets to be the complainant. The other is the defendant.
If the matter involves a different incident and different set of circumstances, the DA are sometimes willing to prosecute on behalf of a former defendant once the case against him has been resolved. If the matter involves the same incident, they won't take it on, especially if the defendant agreed to a disposition.
Once the DA says no to a prosecution your only remedy would be to sue this person in civil court, which generally means hiring a lawyer. If your case is good, you may be able to get one on contingency, meaning you only pay him if he wins your case and then he gets about 40% of your award as his salary. Or, if you have sustained monetary damages, you can bring the case to small claims court where you won't need a lawyer.
I'm sorry for not being able to tell you what you want to hear, but this is how our system works in New York State.