One possibility is that Naruto uses his Shadow Clone Jutsu to create distractions while he rescues Pyrrha from a trap. Since he's so good at this jutsu, he can easily outwit the bad guys. Pyrrha, on the other hand, might be able to assist Naruto once she's free, using her weapon skills.
In a Naruto Saves Pyrrha fanfiction, it could be an interesting crossover. Naruto, with his powerful ninja skills, might save Pyrrha from a variety of threats. Maybe she's in a battle in her own world and Naruto's teleportation jutsu allows him to appear just in time. It could also be that Pyrrha is facing some sort of internal struggle, like self - doubt, and Naruto's indomitable spirit inspires her to overcome it.
Perhaps Naruto saves Shisui from a group of rogue ninjas. He uses his speed and agility, enhanced by his training with Jiraiya, to quickly reach Shisui. His Nine - Tails chakra could also flare up, intimidating the enemies and giving him the power to fight them off.
One possibility is that Anko is poisoned during a mission. Naruto, having learned some medical ninjutsu from Tsunade, uses his skills to find an antidote and save her. He might have to search far and wide, facing various challenges along the way.
In the fanfiction, Sarutobi could be kidnapped by a group of ninjas from another village. Naruto would then embark on a solo mission to rescue him. He'd use his stealth skills and knowledge of the terrain to infiltrate the enemy's hideout and save Sarutobi without being detected.
Perhaps Naruto teams up with Shikamaru. Since Shikamaru was very close to Asuma, they could combine their skills. Naruto's brute strength and Shikamaru's intelligence would make a great duo. They could come up with a complex plan to save Asuma from whatever danger he is in, like a deadly curse or a powerful enemy's attack.
In a 'Goku Saves Naruto' fanfiction, Goku might teach Naruto some of his unique fighting techniques. Since Goku has such a vast knowledge of martial arts and energy control, he could help Naruto become even stronger. For example, he could show Naruto how to better control his chakra using the principles of ki control. And also, Goku's fearless attitude in battle could inspire Naruto to face his enemies more bravely. Goku could also use his Dragon Balls to wish for something that would benefit Naruto or his village, like restoring the damage done by a powerful enemy attack.
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.
Well, Naruto could save a woman who is trapped in a collapsing building during an enemy attack. He could use his super strength and speed to get her out safely. Then, the woman might be so grateful that she offers to help Naruto in his future missions in some way, like providing him with valuable information about the enemies.
Well, Naruto could use his Nine - Tails chakra to create a powerful shield around Mikasa when the Titans are attacking. This would protect her from their attacks. Then he could use his chakra arms to grab onto nearby buildings and swing them both to safety.
In a 'naruto saves boruto fanfiction', Naruto might use his powerful jutsu like Rasengan to fend off enemies threatening Boruto. He could also use his experience and wisdom to guide Boruto out of a difficult situation, perhaps one involving a powerful new villain in the ninja world.