Broken timing belt now I need a new engine

There is no real way to "prove" the mechanic did anything wrong ! Most garages/workshops will guarentee their work for a period of time (usually 90 days on the labor and 12 months on the parts) whichever caused (faulty part/incorrect instalation) your new problem should be covered?

The best you can do is to go to another shop, without mentioning anything about previous work. Get thier prognosis about what is wrong with your car and get an estimate. Keep the new mechanic blind so he can stand trial honestly if need be. You'll need to know exactly what went wrong, and what was offered to you from the first mechanic to fix. If you denied fixing any parts that the first mechanic suggested, then he has some arguments to speak for. If not, then he possibly is at fault, but. If you paid just for a timing belt replacement and only a timing belt replacement, then good luck in court if the timing belt is not at fault. I would not do the job unless I replaced the tensioner, any suspect pulleys etc, including the water pump while I was there. However, if you came to him saying you didn't want to spend any money, and if he did the bare minimum, then again, good luck in court. I hate to be so negative, but I don't know all of the details, it's tricky. You need to compare what was promised against what was delivered. If you paid for what you got, then you have no real case. Let me know more if you can.