Beta badges are earned for three badges earned in private beta. Since you can get Analytical, Autobiographer and Informed badges without any visible activity, this make Beta tag too cheap and not motivating enough.
In my point of view, at least one post should be required in private beta to earn the badge.
Badge limit should be omitted - it favors those who already have an association bonus and can comment and upvote from the very start.
If this is intentional and it's desired to preserve the badge limit as well (if yes, I'm curious about the reason), then raise the limit to 6 badges - with Analytical and Informed it's not so hard to earn 4 more badges even for a newbie and it's not completely for free.