That's exactly the same. But the first sentence is ambiguous, because it could means that you want to make a tattoo on your bosy by yourself, and not that another person do it on you. But equally, both ways are the same and we, the native spanish speakers, interprete those phrases as the same thing (usually the first one is the most used). And although "quiero hacerme un tatuaje" is ambiguous, it takes the ambiguous meaning depending on a specific context.
I hope I'd helped you! :D