The description is weird and hard to understand. The description for Tenacious is
Zero score accepted answers: more than 5 and 20% of total
Unsung Hero is similar, just a little harder.
What are the requirements to get these badges?
The requirement is a little weird to read, but the requirements for Tenacious can be parsed out as follows:
For Unsung Hero, the requirements are similar, but harder:
For example, if you have 6 answers that are +0 and accepted, and 29 total answers, you should obtain a Tenacious badge, since those 6 constitute 20.6% of your answer count. As you can imagine, this is extremely hard to do: only 6 users have ever obtained the Tenacious badge, and only 2 have obtained Unsung Hero on Arqade.