Can i file a law suit against tattoo artist?

Technically you can file suit against anyone however it doesn't seem like you wil have much of a case. The defendant will argue that you should have done more research into the quality of the artist you chose before you put something permanent onto your body. You may be able to get your money back but I'm guessing you didn't pay very much for it based on what you described and after all court costs and lawyer fees you may end up owing money.