Last time I got tattooed my artist was discussing a similar situation with some other tattooers in the shop. This wasn't him it happened to, but someone he knew/knew of:
So a tattooer opens up a shop like almost across the street from the existing shop. Starts trash talking, causing problems, etc., much like you're experiencing. One notable lie that the new tattooer tells about the old is that the older guy has Hep C so people shouldn't get tattooed there. Obviously, old tattooer isn't too pleased about this. His remedy, apparently, was to grab a handful of used needles, walk into new guys shop and stab him with them while he was tattooing a client - "I've got Hep C, do I? Well, now you do too".
The good old days.
I'm not saying you should do this, not at all. You should just keep doing solid work and wait for people to realize the other guy sucks.
Ultimately, and unfortunately, the best action is to "be the better man" and simply continue your good work and don't get drawn in. It is like a playground bully, who wants to engage, and when you ignore them and don't engage, they quit, because there's nothing in it for them. If you don't respond to anything then he doesn't get anything out of it at all - no adrenalin rush, no response, no anticipation of what your reaction might be (or whatever it is that this person gets out of it!). Imagine how excited he gets when the cops show up to his shop, but there's nothing they can do! He can boast to everyone, hopefully (to him) there are people in the shop that see this happen, and he is vindicated, and it is excitement and brings energy to his life that he'd otherwise not have. He's lovin' it.
Sadly, as a business owner and a citizen you have rights and it isn't fair that this guy can do this kind of crap without being stopped, but, without a particular crime being committed, he can. If you can simply hold on, ignore him, wait him out, your work will speak for itself, as will his, and your silence will speak louder than his shouts.
