Hey Rob,
If you hover over the badges in the second screenshot it should show you what's required for that particular badge.
For the supporter badges:
Supporter badge - manually given out for members who are supporting others
StackOverflow - answer three [ringcentral] tagged questions on StackOverflow
Forum - answer three questions on the Developer forum
Blogger - write two blog posts
Soapbox - share a blog post how you feel about RingCentral - good or bad, we want to hear from you
Beta test - participate in a beta test (we should have a couple available soon)
Slides - create two slide decks and post on Slideshare.net or other public site.
Hope this helps,
Mike