Can justice be achieved without violence?

Yes, the criminal justice system is not designed to make justice it is designed to be fair, although it isn't always. It's run by humans you know. The criminal justice system has three elements, legislators to make the laws; police and prosecutors to collect evidence and present at court; and the court process set up to make a decision. These are tools, justice in this system is up to the willingness and abilities of these people (humans).