Today I was looking over the badges page for the badges that I could (maybe one day) get. I noticed that "Beta" badge (that is acquired by users that participated on the beta phase of superuser) could be a badge that I would never get because I didn't even know that Stack Exchange existed on the time of Super Users's beta.
So, there is a way for relatively "new" users to achieve this badge?
No, there is not a change to get the beta badge in retrospect of the beta. However, plenty of SE websites are currently in beta or about to go into beta. (Check the list at Area 51 SE) You could participate in any of those to get the Beta badge there.