The opening of the movie has Yugi beset by monsters conjured from the Puzzle. He transforms into Yami Yugi for the first time, and Yami commands the monsters return from whence they came. They immediately obey.
Joey is implied to beat every single duelist that tried to duel Yugi early on. He even takes an Injection Fairy Lily's direct attack (which can increase from 400 to 3400) and comes out on top, even with the anime having the maximum LP be 4000, not 8000.
One moment we do see is Joey summoning Gilford the Lightning to destroy all of a kid's monsters, then attack for the game.
In Kaiba's duel simulation, he summons the Blue-Eyes Ultimate Dragon and uses Megamorph to increase its attack to 9000. Yami Yugi's response is to sacrifice Ra and Slifer, making Obelisk's attack power infinite. This results in the computer running the simulation overheating. To make it even more awesome, Obelisk was Kaiba's card during Battle City.
Pegasus's first move in his duel against Kaiba is to have the Toon Gemini Elves attack him directly and discard his Monster Reborn.
Kaiba utterly trounces Pegasus with XYZ Dragon Cannon, even though Pegasus brings out his most powerful Toons in one turn, including the Blue-Eyes Toon Dragon. Kaiba bypasses it by destroying Toon World itself.
Kaiba having a straight villainous role is reminiscent of the early manga. He's so eager to take revenge on Yugi, he ends up almost killing him.
When Yami Yugi's down to 1500 LP and is clearly not in the best shape to continue dueling, Kaiba gloats and orders his Blue-Eyes Ultimate Dragon to attack him directly. Yami Yugi gives an epic response.
Yami Yugi: Kaiba, once again your ridiculously over-inflated ego blinds you to the truth! I am far from beaten!
The last blow against Anubis. Faced with a monster with 35000 ATK, Yami quickly deduces what kind of strategy Kaiba had planned to beat him with (using the God Cards), and uses his very last card to activate that strategy in his own favor, returning Obelisk, Slifer and Ra to his side of the field after they had been removed from play, before having them combine for infinite power, finally delivering the last blow. It's so magnificent, the dome around them starts to crack open to reveal boiling lava around the duelists, before the arena erupts in an explosion.
The Blue-Eyes Shining Dragon's final attack was probably the best scene in the whole movie, using its One-Hit Kill attack to destroy Anubis.
Pegasus saves Tea, Mokuba, and Solomon from being crushed by falling debris with his Toons.
As Anubis is about to be revived, Joey and Tristan tell him to back off and move to fight him physically until Anubis's mummies outnumber the heroes.
Joey: I'd stay in that casket if I were you.
In an anime mostly based around card games, they finally got some physical fights in when Tristan and Joey battle Anubis's mummies.
Tea's first reaction upon sensing her friends are in trouble is to jump into the Pyramid and help, and when her physical body enters the pyramid she takes out two of the mummies by accident with a spinning kick.
Kaiba comes closer to beating Yugi in this movie than he ever has, to the point that the only reason he doesn't actually win is due more to New Rules as the Plot Demands than anything else.
Even more awesome in the Japanese version. When he gets a clue that Yugi is telling the truth that he is being controlled, he tries to destroy the Pyramid despite the advantage it gives him, because he wants to win under his own power.
Little Yugi getting tough to protect his protector when he hears Anubis saying he is going to revive using Yami's lifeforce. Yugi isn't going to stand for someone hurting his friend, even if it means going up against a sorcerer.
Yugi: We're not going to stand here while you suck the life out of others to save yourself. We're going to take you down, Anubis!
Anubis reveals himself by growing out of Kaiba's shadow, grabbing him by the head, and throwing him against the floor hard enough to knock him out and injure his arm.
After Anubis blasts Yugi and Kaiba's decks and renders their cards useless, Joey attacks him with his own monsters. When that doesn't work, Pegasus's monsters save the group from the collapsing ceiling.
The epic way Yami Yugi catches the Monster Reborn card after using Double Spell to take it from Kaiba's graveyard.
When Anubis summons himself in real life and turns into a monster, Kaiba throws Yugi the Blue-Eyes Shining Dragon card. Both Yugis use its effect to destroy Anubis, causing him to melt into a pile of shadows before disappearing.