Once you to tribute summon O7, make sure to set down a Riryoku Field to protect it, and use Abyssal Designator to target Blue-Eyes if you haven't already. After Kaiba used both his Enemy Controller and no Blue-Eyes in his deck/hand, Kaiba no longer has any way to beat your O7. Keep destroying his monsters until the last turn and use Vassal to finish the duel. Important: If Kaiba has a set spell/trap card in his field, don't attack him with O7 if you don't have Riryoku Field set the turn before. Make sure that Blue-Eyes is already removed by using Abyssal, otherwise you might have to risk it and just attack.
Since the aim of the deck is to summon O7 early, use the skill to help you with either drawing O7 or get a bubonic vermin to your hand. This is a guaranteed summon if you managed to get 1 vermin and an O7 in your starting hand and you get first turn. Ideally, the best starting hand is something like: 1 Bubonic Vermin, 1 Angel O7, 1/2 Riryoku Field and 1 Abyssal Designator. If you get second turn and get a bubonic, try to switch a card to get Soul Exchange.
Finishing with Vassal or Piranha
You can finish the duel using any card that can deal more than 3,000 - 5,000+. Gravekeeper's Vassal is used here with Union Attack, but you can also use Piranha Army with Rising Energy. This can get you around 4,000 - 5,000 DA depending on the number of glossy cards that you have. Being able to deal more than 5,000 or even 10,000 can get you 7,000+ DA.
If it were possible to trade, I'd gladly trade, since I have more than 3 Enemy Controllers but only 1 Vigilance, which I'd like to have more of for a BEWD deck.
I've been using a slightly different version of this deck. It essentially trades the behemoth and one designator for a second union attack, a third ladybug, and graceful dice (I know, that's 21 cards, but there's nothing I feel comfortable cutting). From my limited testing, it won 2 games with 8K thanks to the bonus and lost the other. Got two copies of champion's vigilance, but no econs.