I noticed the union is not representing the Captain -- he is suing Allegiant on his own.
The meat of the suit is very tricky. US FARs are regulations, not law. Only the regulator (FAA) can enforce FARs, and litigations normally go through the NTSB administrative law process.
A private individual cannot sue another private entity in a State Court on the basis of FARs, e.g., to enforce FARs or to allege interference with PIC authority under 121.533.
So many if not most the Captain's arguments in the civil suit may be thrown out by the Nevada court on the basis of jurisdiction alone.
Another complication is that Nevada is an "at will" employment state. Reading through the suit, I can't find any constructions to specific alleged violations of state employment law. E.g., there is no "Allegiant violated employment law under Nevada Revised Statutes xxx.yyy due to zzz", which is troubling.
The strongest part of his case might be for defamation, as Allegiant seem to have made some procedural errors when firing him.