To become a beast is:
1.to become real good at something i.e. video games, the guitar, football game
2.to become ferocious and belligerent and to engage in actions of violence or disrespect.
'Beasting' or 'beasting it' is to engage in actions which demonstrate any of the two before stated definitions.
1. Dang, i was playing Halo with that cat and he started beasting it like a mother fucker. He killed everybody, dawg!
2.yo, cuz, when he fount out his girl was doin that mofo down the street, he started beasting it on them people walking by.