A possible plot could be that Percy and Annabeth are separated in Tartarus for a while. Percy has to find his way through a maze - like area filled with deadly traps while Annabeth is being chased by a group of vengeful spirits. Eventually, they reunite and combine their knowledge and skills to face a powerful Titan who has been ruling over a part of Tartarus and is trying to stop them from escaping.
They could discover a lost civilization in Tartarus. This civilization might have a way to manipulate the very fabric of Tartarus itself. Percy and Annabeth would then have to learn the ways of this civilization in order to use it to their advantage. Maybe they have to earn the trust of the civilization's leaders by helping them with their own internal problems first.
In some fanfictions, a possible plot development is that Percy and Annabeth discover a long - lost secret or power within Tartarus. This could be something that gives them an edge in their fight to escape or a knowledge that changes their perspective on the whole Greek mythology world. As they explore Tartarus, they may find ancient artifacts or meet forgotten gods who have been trapped there for ages. These encounters can lead to unexpected alliances and revelations that add depth to the story.
One interesting scenario could be Percy and Annabeth finding a hidden, powerful weapon in Tartarus that gives them an edge against the monsters there. Maybe it's a sword that can cut through the very fabric of Tartarus's darkness.
A great plot could involve Percy finding a way to use the unique environment of Tartarus to his advantage. For example, there could be some sort of energy in Tartarus that he discovers he can harness to become stronger, but it has a dangerous side - like it might slowly corrupt him. He then has to struggle with the decision of whether to keep using it to get out or resist it.
One idea could be Percy having to prove himself in the Underworld. Since he's the son of Tartarus, he might face unique challenges from the other denizens who fear or distrust him. Maybe he has to compete in some sort of underworldly tournament to gain respect.
Another plot could be that something from Tartarus has followed Percy out. A small, malevolent creature that starts causing trouble in Camp Half - Blood. Percy feels responsible for it and has to find a way to send it back to Tartarus without putting everyone in danger.
One interesting plotline could be their struggle against the various monsters in Tartarus. For example, facing off against the giants or other terrifying creatures that lurk there. Another could be their search for a way out while dealing with the psychological toll of being in such a dark and desolate place.
One more plot idea could be that Percy and Annabeth are somehow affected by the dark magic of Tartarus. It changes them in some way, either physically or mentally. They then have to deal with these changes while still trying to escape. This could lead to some really intense internal and external conflicts as they struggle to stay true to themselves and also find a way out of Tartarus.
A plot could be set in a post - apocalyptic world where Percy and Annabeth are on opposite sides at first due to some misunderstanding. As the story progresses, they realize they need to work together to face the real threats in this dark new world.
One plot idea could be that Percy is so caught up in his own heroic deeds and adventures that he completely misses all of Annabeth's subtle hints of her feelings for him. Meanwhile, Annabeth tries different ways to get his attention, like helping him with his studies in a very flirtatious manner, but Percy just thinks she's being a good friend. Another could be Percy getting into a situation where he has to protect Annabeth without realizing his true feelings for her are deeper than friendship, and throughout the fanfic, his obliviousness slowly starts to fade as he gets closer to her in the face of danger.
In a fanfiction about their bickering, a plot could be centered around a magical item. Let's say they find a new weapon or artifact. Percy wants to use it right away to test its power, but Annabeth is worried about the potential consequences and unknown abilities of the item. This leads to their bickering. Additionally, they could bicker about their relationships with other characters. For instance, Percy is friendly with a new demigod who Annabeth is a bit suspicious of, and this causes tension and arguments between them.