What can I do to get my money back for a bad tattoo job?

If the job is not merely not as good as you'd like but is unprofessional--does not meet minimal professional standards--you can likely get your money back (though you'd have to show in court that the job was that unprofessional--unless the issue if very obvious, that could mean having some other tatoo artist testify for you). But if it's minimal commercially or acceptable quality, then while it's unfortunate, you would not be able to get the money back. The way to think of it is this: tatoos obviously come in a range of quality: even among ones done by experienced professionals, some are better than others. If the tatoo you received is within the range of what professionals do, even if it's at the bottom of that range, they don't have to return your money. Only if its below professional grade, or has an obvious error (e.g. you wanted a tatoo with your significant other's name "Jenny" but they spelled it "Jonny"; or like that "Milky Way" commercial, spelled "No Regrets" as "No Regerts") are you entitled to your money back. 
Also bear in mind that if they won't voluntarily pay, you'd have to sue. Even in small claims court as your own attorney ("pro se") you'll still spend time at the least--assume you'll give up a day (at least) to the lawsuit and decide if that time is worth the money you hope to get back.