I think the most exciting part would be when Naruto taps into his full power, perhaps the Nine - Tails' chakra or Sage Mode, to overpower Orochimaru. He'd be in a state of pure determination, and seeing him go all - out against Orochimaru to save Hinata would be really thrilling. Also, Hinata might show some hidden strength or courage during this part, making it even more exciting as they work together to overcome Orochimaru.
Well, Naruto might discover some new Orochimaru's plan during the rescue. Maybe Orochimaru was trying to use Hinata to get some information about the Byakugan. After saving Hinata, Naruto could go on a mission to stop Orochimaru from achieving this goal with the help of his friends like Sasuke and Sakura.
One possible plot twist could be that Orochimaru was actually being controlled by a greater evil, and Naruto has to not only save Hinata but also deal with this hidden threat. Maybe Orochimaru was forced to target Hinata to draw Naruto out for this other entity's purposes.
I'm sorry I haven't read a specific fanfiction with this exact plot, but generally in such a scenario, Naruto would probably use his powerful jutsu like Rasengan. He'd sense Hinata in danger from Orochimaru, rush to the scene, and engage in a fierce battle with Orochimaru to rescue Hinata. Maybe he'd also get some help from his friends along the way.
The most exciting part could be when Naruto uses his new and powerful jutsu that he has just mastered to save Tsume at the very last moment. It would be a display of his growth as a ninja.
One possible scenario could be Naruto arriving just in time as Orochimaru is about to perform a dangerous jutsu on Sasuke. Naruto uses his new Rasengan variant, overpowering Orochimaru and rescuing Sasuke. It would be a very action - packed moment.
One possibility is that Naruto discovers Orochimaru's lair through some clever detective work. He then sneaks in, avoiding all the traps. When he sees Orochimaru about to perform some sort of experiment on Hinata, Naruto jumps in and starts fighting. He might transform into his Nine - Tails Chakra Mode to gain an edge in the battle and save Hinata.
Well, if Naruto saves Hinata from Orochimaru in a fanfic, it might start with Hinata being captured by Orochimaru's minions. Naruto would immediately go on a rescue mission. He'd probably fight through Orochimaru's various snake - based defenses. And when he finally reaches Hinata, he'd defeat Orochimaru with a powerful Rasengan, and then carry Hinata to safety.
A plot could be that there's a tournament - like situation where Neji and Hinata are pitted against each other, but Neji goes too far. Naruto, who has feelings for Hinata (even if he hasn't fully realized it yet), jumps into the fray. He uses his shadow clones to confuse Neji and then uses his Rasenshuriken in a non - lethal way to stop Neji. This not only saves Hinata but also starts a new chapter in their relationships, with Naruto becoming more aware of his feelings for Hinata and Neji starting to question his own actions and beliefs.
The plot could start with Hinata being alone in a secluded part of the village and the bullies spotting her. They start to tease her about her family or her lack of confidence. Naruto, who has a strong sense of justice, comes across the scene. He uses his skills and his reputation as a hero to scare the bullies away. After that, Hinata and Naruto have a moment where Hinata thanks Naruto, and Naruto encourages her to be more assertive.
It could also result in a change in the way the village views their relationship. Since Naruto is a hero, his saving of Hinata would be a big deal. This could lead to the village elders or the people in general being more accepting of a possible romantic relationship between them. For example, they might start to see Hinata as a more important figure in Naruto's life and give her more respect.