In all of my walking around BA I can think of only one, down the street from the IFTA theater on Boulogne Sur Mer near Corrientes. It looked well established. But there is probably a whole street of tattoo parlors somewhere in BA.
Here area few, Herná Coretta, he has a shop on Cabildo in Belgrano. You can visit him at www.corettatatoo.com, I have loads of tattoos and am currently working on being a tattoo artist. A lot of tattoos I have seen here are not that great in terms of the work. But I have seen a few of Coretta's tattoos and they are flawless. Then there is Nazareno, www.tattoosbynaza.com he is in a completely different level in terms of being an artist. For Naza you have to email first and then a consultation is set up (which is AR$300 and will be taken off of the price of your tattoo). At the moment, or when I last checked he did not have any availability until March, but take a look at his page, it is pretty incredible.
I think that Coretta may be a bit more available but I am not sure. I would stay away from the majority of tattoo artists at Bond Street, unless you have someone recommend you one in particular. They don't always do everything up to code and I have seen a lot of crap tattoos done at Bond Street, ink that fades, scarring, shaky line work.
So best of luck and there are good tattoo artists here, you just have to look.
Yes, I know the shop you are talking about. I live really close to it. It is called ''Historia de Mi Vida" and is in the 1900 block of Scalabrini Ortiz which I think is between Soler and Guatemala. I keep meaning to go in a have a look. The sign on the window "Of course it hurts" is pretty funny.