Funnily enough the prince is a part of that dickbaggery. The whole bet was his idea, after all. Without the prince's bet, the whole student representative confrontation might have stopped at nothing but badmouthing Clarisse just that one time. It's quite likely Belville wouldn't have dared to do it twice knowing Clarisse is under the prince's protection, in one way or another. So, that's it. But now, with the prince forcing the bet on them for his own amusement, Belville has got absolutely nothing to lose and will go all out to be as villainous as he needs to be to win.
That being said, bad luck for Eugenie. If Belville loses, she will get rid of him, but that wouldn't happen before his meeting with the rotten queen. So, she hasn't got much of a choice for the time being. If Belville wins and folks learn she trained him, what will happen to her? The prince might see to it that her ending won't be good. He's the psychopath king's son.