Recapitulation.

Mai has activated the "Seal of Oreichalcos" against Jounouchi, having joined Doma in the search for power great enough to ensure that she could never be defeated.
- The Duel is observed by Yami, Anzu, Honda, Valon and Rafael. Insector Haga and Dinosaur Ryuzaki also watch the Duel from behind the security gate.

On The Very Edge.

Jounouchi's turns up until now have been half-hearted because he does not want to defeat her in such conditions. However, with only 200 Life Points left, he has realized that he must duel with all he has in order to reach her. With this, he takes his next turn, dealing the only damage Mai has taken so far.
She calmy responds by summoning Harpie's Pet Dragon, increasing its attack power to overwhelming levels. Valon looks on eagerly and sure of her victory, while Rafael admits he was expecting more out of Jounouchi.
Jounouchi responds by activating a gambling Trap. He has a one-in-three chance of Negating her Attack; if he misses, the Attack will go through unchecked. He succeeds, but his Trap's other effect gives Mai back two Cards that wrecked his forces in previous turns.
Jounouchi switches to defensive playing, and although his Life Points stay safe, his attempts to use effects on her attack forces are each parried by her new cards.
Rather than risk attacking into a dangerous effect, Mai draws on her newfound power, using her retrieved Harpie Lady Phoenix Formation to go for the kill. Jounouchi saw this coming, and his defensive effect stops her chance of a finishing move. However, he is nearly out of resources, and he has not decreased her power at all.

Backed into such a corner, he notices a bright light coming from his Deck. He is transported to another world, arriving at a crystal statue of a dragon with a sword stuck in it. He removes the sword, freeing "The Claw of Hermos" and bonding to it. In the real world again, he takes his Turn, Drawing and revealing Hermos, the newest power of his Deck.
Rafael's Oreichalcos fragments shines and he realizes it must be the "Legendary Dragon", turning Valon nervous.

Since Mai has at least 2 more Monsters than him in play, Jounouchi is able to use "The Fiend Megacyber's" Special Ability and Special Summon it from his Hand to the Field (2200 ATK / 1200 DEF).
Uses "The Fiend Megacyber" to Attack & Destroy one "Harpie Lady" (Mai: 4000 → 3600 Life Points).
Sets a Card.

Tributes two of her four tokens to Summon "Harpie's Pet Dragon" (2000 → 2500 ATK / 2500 DEF). Since there are three "Harpie Ladies" on the field, Mai's Dragon Special Ability allows it to receive a further +900 ATK boost ("Harpie's Pet Dragon": 2500 → 3400 ATK / 2500 DEF).
Attacks "The Fiend Megacyber" with "Harpie's Pet Dragon", but Jounouchi Activates Trap Card "Compensation Mediation": Mai picks two Cards from her Graveyard and puts them, along with "Compensation Mediation", Face-Down on the Field; Jounouchi picks one Card and chooses "Compensation Mediation": Mai's Attack is Negated and she returns her two chosen Cards ("Harpie Lady Phoenix Formation" and "Harpie Lady Sparrow Formation") back to the top of her Deck.
Moves her "Harpie Lady" to the Spell & Trap Card Zone.
Sets Two Cards.

During Mai's Draw Phase Jounouchi Activates Trap Card "Drop Off", but Mai Negates it with Counter Trap Card "Trap Jammer" (NOTE: In the real game "Trap Jammer" can only be Activated during the Battle Phase).
Sets a Card.
Uses "Harpie's Pet Dragon" to Attack & Destroy Jounouchi's "The Fiend Megacyber".
Uses "Harpie Lady" to Attack & Destroy Jounouchi's Face-Down Monster: it's revealed to be "Fiber Jar" (500 ATK / 500 DEF). Mai Negates its Effect with Counter Trap Card "Harpie's Feather Storm".

Instead of Attacking, Activates Spell Card "Harpie Lady Phoenix Formation", Destroying Jounouchi's Face-Down Monster: it's revealed to be "Neko Mane King", whose Effect Ends Mai's Turn. Since "Neko Mane King" has 0 ATK, the Effect of "Harpie Lady Phoenix Formation" deals Jounouchi 0 Damage.

Jounouchi & Yami have a vision, and Jounouchi unlocks the "The Claw of Hermos". It is the Card he Draws during his Draw Phase.