I'm not sure about the exact plot as it depends on the specific fanfiction. But generally, it might involve Sakura using her skills, perhaps medical ninjutsu or her combat abilities, to rescue members of the Akatsuki from a dangerous situation, like a powerful enemy or a deadly trap.
Obviously, Sakura is one of the main characters as the title implies she is the one doing the saving. And the members of the Akatsuki would also be main characters, such as Itachi, Kisame, and others depending on how the fanfiction is written.
Perhaps the Akatsuki saves Naruto because they want to use him for their own purposes in a different way. Instead of killing him or using him as a weapon against Konoha in the traditional sense, they might save him from a situation where he is being hunted by other forces. Then they plan to train him or manipulate him in a new way to further their own goals, like changing the power structure of the ninja world.
I'm not sure specifically as there could be many different versions of this fanfiction. It might involve Sakura having some sort of relationship or adventure within the Akatsuki group. Maybe she could be a spy among them, or perhaps she gets involved in their various missions and power struggles in a unique way.
Sakura might be very cautious at first. She's heard about the Akatsuki's bad reputation, so she would keep her distance. For example, if she sees an Akatsuki member lurking around school, she'd probably try to avoid them and alert the proper authorities, like the school security or her ninja mentors if it's in a Naruto - like world with ninja training in high school.
Obviously, Naruto is one of the main characters. He is the one being saved. And then, members of the Akatsuki like Itachi, Kisame, or Pain would likely be main characters as well. Itachi, for instance, has his own complex motives and backstory that could play into the story of saving Naruto. Kisame is a powerful and loyal member of the Akatsuki who could be involved in the rescue mission. Pain, as the leader in some cases, would also have a significant role in deciding whether or not to save Naruto and how to go about it.
The Akatsuki members would be the main ones. It could include Itachi, who is known for his complex character and powerful abilities. His relationship with Sakura could be an interesting aspect, whether it's one of mutual respect or a more adversarial one.
Itachi. He has his own moral code and he might see something in Chibi Sakura that reminds him of his own will to protect. He could form an alliance with her if he believes it would be for the greater good, like stopping the more extreme members of Akatsuki from causing too much destruction.
In Akatsuki lemon fanfiction involving Sakura Haruno, the story could take on many twists. The Akatsuki is known for its dark and mysterious nature. Sakura, being a strong - willed character from Konoha, would be in a very different environment. The 'lemon' part might introduce some unorthodox relationships. Maybe she falls in love with a member who she was initially supposed to fight against. This could lead to internal conflicts within her, as she has to balance her loyalty to Konoha with her new - found feelings.
In this fanfiction, Sakura might get involved in a school project that has a big impact on the whole Akatsuki High School. She could use her unique skills, like her intelligence or her kind heart, to bring about positive change. For instance, she might organize a charity event to raise funds for a local cause and in the process, unites the whole school.