To get Tesla, earn 10,000,000+ energy points. One way to get this badge is to watch at least videos 5000 videos and get the 299,792,458 Meters per Second badge in 300+ exercises. This is the only Black Hole Badge which does not give a user any energy points when obtained.
Master an unknown amount of unique skills to get this badge (used to be 150, then 500, and now is believed to be 1000.) Ben Eater got this badge. People think that he accidentally gave it to himself.
Unknown, supposedly, Peter Collingridge, a user that became a Khan Academy employee, knows its requirements, but hasn't announced them. We are still looking at the evidence in the HTML code.
To to earn Galileo, user has to become a content creator who records 3000 videos on Khan Academy. Because of the low demand for this position, it is impossible for most members to acquire the badge