"Never don't give up" sounds like it should be the name of a parody action movie, not a slogan on your arm. I like to have a little faith in humanity where I imagine that this guy is very funny and got an ironic tattoo. Maybe "never don't give up" is something one of their friends said and has since become an inside joke. Truth is, that's probably not the case. This is most likely the work of a fool who thought he was telling people not to give up, when in actuality he was telling them the exact opposite.
Due to the double negatives of 'never' and 'don't,' we have a statement that says you should always give up. Not just sometimes, but always. Come to think of it, that doesn't sound like too bad of a life.