* "The Avatar State" (Book 2, Episode 10): This is the first time Zuko and Ozai face each other in a full-fledged fight. While Zuko does manage to land a blow, Ozai ultimately overpowers him, showcasing the immense power gap between them. This episode is crucial as it highlights Zuko's desperation to prove himself to his father, but also the futility of trying to win against such an overwhelming force.
* "The Day of Black Sun" (Book 2, Episode 19): Zuko confronts his father during the solar eclipse, hoping to finally defeat him. However, Ozai is still far too powerful, and Zuko is ultimately defeated and left for dead. This battle highlights the destructive nature of Ozai's power and the intense emotional turmoil Zuko endures.
* "Sozin's Comet, Part 3: The Firelord" (Book 3, Episode 20): This is the final confrontation between Zuko and his father, where Zuko, aided by the Avatar Aang, finally manages to defeat Ozai. This battle is crucial for the story's climax, as it marks the end of Ozai's reign and the beginning of a new era.
It's worth noting that these are just some of the episodes where Zuko and Ozai fight. There are other smaller confrontations throughout the series, including in episodes like "The Blue Spirit" (Book 1, Episode 7), where Zuko attempts to capture Aang but is stopped by his father.
To understand the full context of their relationship and the significance of their battles, it's best to watch the entire series.