Arbitration is an alternative to going to court, so you can't file one in court.
You also generally don't have a choice. If the contract provides for arbitration you must arbitrate, if it doesn't you must bring a court case.
You file a civil court case by preparing and filing a complaint and draft summons with the clerk of the court, having the clerk of the court authorize the summons, having a deputy sheriff or a process server hand deliver the summons authorized by the clerk and the complaint to the defendant, and then following the court rules from there. This is quite difficult, but if no lawyer will take your case, you may have little choice.
This seems like the simplest thing to me, have expert witness, have
the contract, have pictures, have audio recordings and witnesses that
worked for him that can attest to the deliberateness of the actions.
For what it is worth, this is not at all simple. It is possible, but that is something entirely different. There would also have to be considerable legal research and briefing to determine that the elements of fraud were satisfied and were not barred by another legal doctrine.
Honestly, $7,500 to $15,000 of legal fees as an estimate seems very low to me, and that means 30-60 hours or so of legal work. Doing it without a lawyer would take at least twice that many hours, so maybe 60-120 hours of your time, and would be much less likely to obtain a successful result. Of course, if you can convince the other side (while you are legally represented) that you will carry the case to completion, there is a good chance that they will settle, because they also don't want to spend large amounts of legal fees on a small dispute.