A plotline could be Percy having to face his own fears and insecurities while being tortured. Maybe he starts to doubt his abilities and heroism. But as the story progresses, he overcomes these doubts through his willpower. Also, the fanfic could explore how the torture affects his relationship with the gods. He might feel betrayed by them for allowing him to end up in Tartarus and this could lead to a change in his loyalty or attitude towards them.
He might use his powers in creative ways to lessen the impact of the torture. For instance, if the torture involves some form of mental attack, he could try to use his connection to water to calm his mind. Also, his demigod abilities, like his superhuman strength and agility, could help him physically resist some of the more brutal forms of torture to a certain extent. And he may also draw strength from the memories of his past victories and the people he has saved.
There's also the possibility that a new character could be Percy's savior. Maybe a powerful and mysterious demigod who has been hiding their powers all this time. This character could have some special connection to Tartarus or a unique ability that allows them to enter the realm without being immediately overpowered. They could be drawn to Percy's plight and decide to risk everything to save him.
In some fanfictions, Percy's torture in Tartarus could be part of a grander scheme. For example, an enemy on the surface world has made a deal with the forces of Tartarus to weaken Percy. As he endures the torture, he gradually uncovers the conspiracy and tries to find a way to not only escape but also stop those who sent him there. His friends, unaware of his situation at first, start to suspect something is wrong and embark on a quest to find out what happened to him and rescue him.
Maybe it's part of a plot to have Percy gain some sort of power or knowledge. In many fictional stories, a character has to go through great pain and suffering before emerging stronger or wiser. The torture in Tartarus could be a way to set up this transformation for Percy.
Nyx could be a great main antagonist. She's a primordial goddess of the night and Tartarus is her domain in a way. She might see Percy and his friends as intruders and try to stop them from leaving or achieving their goals. She could use her power over darkness and the unknown to create all sorts of obstacles for them.
Perhaps he could make an alliance with some of the less hostile creatures in Tartarus. There might be beings who are also tired of the chaos and want to help Percy in exchange for something, like a promise to free them from Tartarus if he ever gets the chance. Percy is known for his charisma and ability to make friends, even in the most unlikely situations.
Percy might endure it through his own stubborn will. He's a demigod used to facing tough situations. In this fanfiction, he could be using his past experiences of fighting monsters and surviving hardships. He might tell himself that he's been through worse and this is just another trial he has to pass. So he grits his teeth and bears it as best he can, even when the torture in Tartarus is beyond what he's ever faced before.
He could find some minor gods or goddesses who have been banished to Tartarus. They might see Percy as a way to get revenge on the Olympians or simply a means to escape. Another potential ally could be some of the more intelligent monsters, like a centaur who has been there for a long time and has knowledge of the place.
In a Percy Jackson Tartarus fanfic, a great plot could be centered around Tartarus corrupting the very essence of Percy's powers. He starts to lose control of his water - based abilities and instead they become tainted with the darkness of Tartarus. Percy then has to go on a journey within Tartarus to find a way to cleanse his powers, all while being hunted by the most dangerous creatures that lurk in the abyss.