In this type of fanfiction, Percy could also endure the torture by focusing on his sense of purpose. He may be thinking about protecting the world from the threats that lurk in Tartarus. His sense of heroism doesn't allow him to give in easily. He might be constantly reminding himself that if he breaks, then all those he loves and the entire world could be in danger. So he uses this as a mental shield against the physical and mental pain of the torture.
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 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.
Well, Percy might endure it through his natural demigod abilities. His connection to the water could potentially be a source of comfort or even a way to resist Kronos' power to some extent. Maybe he can draw strength from the water element around him, even in the midst of torture. Also, his combat skills might help him brace himself mentally, as he's used to facing tough situations in battles.
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.
Percy might become more resilient. The constant torture in Tartarus forces him to dig deep within himself to find the strength to survive. He learns to endure pain and hardship in ways he never had to before, which toughens his mental state.
In some fanfictions, Percy might use his water - controlling abilities in unique ways. He could manipulate the rivers of Tartarus, like the Phlegethon, to create distractions or even use the power of the water to propel himself out. Maybe he also forms alliances with some minor creatures in Tartarus that are not as hostile as the main threats and they help him find a hidden passage.
In some fanfictions, Percy might gain power in Tartarus through facing and overcoming numerous deadly challenges. For example, by defeating powerful monsters that inhabit Tartarus, he could absorb some of their essence or gain knowledge from them which then transforms into power. Another way could be through making pacts with certain entities in Tartarus in exchange for power, although this would likely come with a price.
In some fanfictions, Percy might get hurt in Tartarus due to the numerous and powerful monsters there. For example, he could be injured by the Empousai. Their sharp claws and ability to move quickly can catch Percy off - guard, leading to cuts and bruises.
Another scenario could be that Percy is forced to endure extreme environmental conditions in Tartarus. The place is known for its intense heat, toxic fumes, and jagged terrain. He might be made to traverse through burning lava fields or climb sheer cliffs while being constantly weakened by the poisonous air, all of which would be a form of torture.
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.
It could be the traditional villains from the original story. Maybe some of the old enemies of Percy who have a vendetta against him. For example, the Titans or some rogue demigods who oppose him for power or personal reasons.