According to the description of the tenacious badge:
Zero score accepted answers: more than 5 and 20% of total.
"Zero score" make sense; the answer was accepted without an up vote.
But what does "more than 5 and 20% of total" mean?
It means you need to have six or more accepted zero score answers, and those must at least make up 20% of all your accepted answers to get the badge.
- silver; awarded once
- Have more than five accepted answers with a score of zero, and have those zero-score accepted answers account for at least 20% of all your accepted answers