Uh, sorry...but you most definitely will have to prove it. I worked for 20+ years in third party debt collection & as a legal assistant in a law firm specializing in civil litigation. It's possible that it won't even go before a judge (ie, a trial) if he doesn't file a defence, but because it's for damages, the clerk will likely not sign default judgment in that event, it will have to go to an assessment hearing, which is before a judge where you will have to prove your damages. If he DOES file a defence, you will have to prove that he deliberately did whatever you are alleging & proving intent is pretty difficult. Also, you sound like you are proposing to sue the mechanic, but not the shop? That's likely a non-starter.
BTW, the biggest mistakes people make when trying to sue their own claims is not researching how to collect before they do it, not knowing which entity to sue & not knowing enough about how the process works. You don't just decide to sue someone, then bitch because you have no way of collecting. You have to plan this out before you do it to know if it's going to be worth your time & money. Unfortunately, too many people get caught up in "it's the principle of it" mentality to do things right. JMO.