What are the requirements for the beta badge? I know that I have to actively participate in the private beta. What does actively mean? Is there a minimum number of questions, etc?
A full list of badges can be found on Meta.SE
The user must earn at least three bronze badges during the private beta period. The badge will be awarded when we move into public beta.
Since the answer isn't really given elsewhere, on purpose, I'll chime in with what I remember being told when commiting to another beta: one must at least post 10 answers and/or questions for the commitment to be considere fullfilled.
I don't know if it's correct or applies to he beta badge, and I wouldn't bother too much. More participating and less worrying should get the job done.