Embarrassingly, I think I earned them, but obviously not. What's it take?
- Tenacious: Zero score accepted answers: more than 5 and 20% of total
- Unsung Hero: Zero score accepted answers: more than 10 and 25% of total
The key words are "accepted answers" so the OP has to give you the checkmark, and "25% of total" which means at least 1/4 of your answers need to be in this state. Today, not a single person the site has this badge, because an answer that gets accepted almost always gets at least one vote. And for those correct answers that don't get a +1, they often don't get an "accepted" check because we have a lot of abandoned questions where the OP doesn't return to accept your answer.