As with Cover-Up in most cases, Yes, a bad Tattoo can be fixed. Talk to your Artist as in some cases you may be better covering over rather than attempting to rectify your current design. If you have bad scarring a re-work or cover up will not help. Listen to the advise you are being given, a good artist will only tell you the truth. Again, check the Artists portfolio for examples of Re-Working - it is a skill.

Check out the example below and Big Petes Re-Work Gallery for extensive examples.