There's not much in there yet about the overarching story with Brainiac and the future and all that yet, it's mostly just smaller mission arcs right now. The tutorials open up with you escaping from Brainiac's ship with your new powers and all, but after that it's mostly just smaller arcs in the beta. Supposedly there's going to be a bunch more of that by the time the game is released, but the Beta is more just for testing mechanics and all that so there isn't much of the big story...yet. Kinda a bummer, but whatever, it's free.
-Gary