I was repairing a vehicle with the deal of purchase after it ran. So I paid out of pocket paid for all parts & also did the work myself. But then after I fixed and serviced the vehicle the owner backed out. Can I file a mechanic lien to get back what I paid out for parts & for my hours?
You can't put a mechanics lien on a vehicle in arizona. Mechanic's liens are a legal term defined under the statute and only apply to real property.
The type of lien you are looking to impose is generally called a "garageman's lien." The provisions for imposing a gragman's lien are found in A.R.S. section 33-1022. It is confusing that the statutes refer to mechanis liens in a context that don't relate to auto mechanics at all.
You will need to speak with an attorney that does garageman's liens to determine what, if any, rights you have. If you have possession of the car and are entitled to sell it to a different purchaser, that is propbably your best option.