Sasuke could be the one to save Naruto. Despite their past differences, Sasuke still has a connection to Naruto. He might sense Naruto's danger and rush to his aid, using his Sharingan to find a way to safely get Naruto back up from the bottom of the cliff.
It could be Kakashi. Kakashi is always looking out for his students. He might use his ninja dogs to track Naruto's fall and then use his teleportation jutsu to reach Naruto just in time. He would then use his medical skills to treat any injuries Naruto might have sustained.
Sasuke could save him. Despite their differences, Sasuke might still have that underlying bond with Naruto and show up just in time to catch him or pull him to safety.
One possible reason could be Naruto's natural sense of justice. He can't stand to see a child in danger, and Koyuki being a child at that time, Naruto's heroic nature kicks in. He has always been the type to help those in need.
Well, in most cases, Naruto might use his signature jutsu like the Rasengan. He could either deflect the fire ball with it or use his incredible speed to get to Ami before the fire ball hits her. Maybe he also uses his shadow clones to create a distraction for the attacker while he rescues Ami.
Sakura could be the one to save Naruto. She is a skilled medical ninja. She could use her medical jutsu to keep Naruto alive even while he is crushed. Then, with the help of others like Kakashi, they could figure out a way to remove the rock and fully heal Naruto.
Sakura would be a likely candidate. As a skilled medical ninja, she has the knowledge and ability to diagnose the poison and attempt to create an antidote.
Well, in many fanfictions, Naruto might use his ninja skills. He could use his speed to reach Artemis quickly if she's in danger, like if she's being attacked by some powerful enemy. His shadow clone jutsu could also be useful to distract the foes while he rescues her.
Well, it could be that Naruto has developed a new and powerful form in the fanfiction. With this form, he emits an intense chakra that scares off the Cloud attackers who are after Hinata. His speed and strength in this new form are so great that he can easily reach Hinata and get her to safety before the Cloud ninjas can react.
Well, it could be that Mikoto is trapped in a dangerous situation like a collapsing building or a genjutsu. Naruto, with his strong will and powerful chakra, breaks the genjutsu or rescues her from the rubble. He might sense her distress using his Sage Mode or his connection to the Nine - Tails' chakra and rush to her aid.
Well, in many fanfictions, Naruto might use his signature jutsus like the Rasengan. He could sense the danger the woman is in using his enhanced ninja senses and then quickly dash in to counter Rizevim's attack with his powerful moves, overpowering Rizevim and rescuing the woman.
Well, Naruto is known for his quick thinking. So perhaps he quickly assesses the situation and uses the surrounding environment to his advantage. For example, if there's a water source nearby, he could use his water jutsu skills (if he has them in that fanfiction) to counter the fireball and save Ami. Or he might even use his body as a shield if it comes down to it, relying on his Uzumaki durability.