The plan with this deck is to fulfill your Quest with Cataclysm at turn 4. You need to mulligan for the right cards, but you also see early when you don't have the right cards so you can restart.
You need one Cataclysm to play on turn 4 and if somehow possible Malchezaar's Imp to play on turn 3, so you refill your hand with cards after you played Cataclysm. If you draw Bloodreaver Gul'dan before you played Cataclysm you can start all over again, it won't work if you have to throw him away.
Once you have this setup, you are hopefully going to win! Trade your Minions with his and use Siphon Soul to remove is big dragons like Ysera. You don't have to play all the cards that help Chromaggus immediately but try to keep cards of one type e.g. his Minions cost 3 less. Chromaggus will use up all his Cards so it won't matter that he gets his Minions for free because he can only play the one he just draw.