Before you can even dream of earning this trophy, you first must complete story mode at least once. It doesn't matter who you choose to fight as, once you finish your first run of story you then unlock Brainiac.
Beta Strike is performed by pressing
. I think it becomes more powerful if you hold the button longer, but all you need to do is KO an opponent with this move.
Set up either a versus with 2 controllers or a Very Easy Single Fight. Pick Brainiac and any other opponent, chip their health down to as low as possible without winning and then press
to perform this move. The trophy should unlock after.