Just out of curiosity, since this is the first private beta I've participated in- what are the requirements to get the beta badge? The description says "actively participated"; what metric dictates how "active" one's participation is?
I think the recipe is kept secret, to avoid gaming the system.
The badge is there to incentivise active contributions to the site during the private beta.
That might (or might not) include a combination of some, none or all of the following activities: posting expert-level questions and answers; commenting; editing; participating here in meta; participating in chat; flagging; up-voting, down-voting, voting to close, voting to re-open, voting to delete, voting to undelete, waving your hands in the air like you just don't care.
OK, the last one's flippant - and it's there to illustrate that I don't actually know - only the SE Inc staff do, and they're not telling. It's secret.
So just keep actively contributing quality content, and actively participating in all the site activities - posting, voting, commenting, flagging, meta, chat - and let the badge come to you in its own due course.
In the end, beta badges were awarded to 33 users.