What is the way to open quiz reviewer badge?

Answer 1

//Nope not only for moderators, if you too moderate quizzes you can get one but it takes time
https://www.sololearn.com/discuss/568849/?ref=app

Answer 2

If you click in your profile -> badges -> click on the symbol on the right side -> list of all badges with description:

"Exclusive badge, handed out to community members who moderate user-generated quizzes"