I just acquired the Tenacious badge but the description is leaving me wondering what exactly I've done to acquire it.
Zero score accepted answers: more than 5 and 20% of total.
Basically, you have a ton of answers that have a score of zero and are also accepted.
In particular, you have more than 5 answers that have a score of zero and are accepted. And, those zero-score-accepted answers make up at least 20% of your total answers.
This picture could help:
You should have this at least 5 times and 20% of your total answers. In other words, pray to not be upvoted on your accepted answers :)