Percy's strong will and determination play a huge role. He constantly reminds himself of his friends and family waiting for him outside Tartarus. This mental strength gives him the motivation to keep going. Additionally, he could discover some hidden powers or artifacts within Tartarus that aid in his survival. For example, he might find a magical item that can heal his wounds or protect him from the worst of Tartarus' dangers.
He might rely on his skills and the powers he already has. His control over water could help him find sources of water in Tartarus for survival. Also, his combat skills would be crucial in fending off the various monsters there.
In some fanfictions, Percy forms unexpected alliances. He could team up with other banished or lost souls in Tartarus who have their own reasons to survive. Together, they share knowledge and resources, which helps Percy stay alive. Maybe he even befriends some of the less hostile creatures in Tartarus. His ability to empathize with others, even in that harsh place, gives him an edge in survival.
He might rely on his powers. Percy is a son of Poseidon, so his control over water could be crucial. He could use water sources in Tartarus, if any, to heal himself, create barriers, or even find a way to escape. For example, he could manipulate the Styx water to his advantage.
He uses his wits. Percy has always been clever, and in Tartarus, he'd use that to his advantage. He'd find ways to outsmart the monsters, like using the environment against them.
First of all, Percy's resourcefulness would come into play. He would probably try to make allies among the less - hostile creatures in Tartarus. He has a way of befriending those who are often overlooked. Also, he would use his knowledge of Greek mythology. Since he knows about many of the monsters and their weaknesses from his studies, he can use this knowledge to survive. His connection to his friends, even if they are far away, might also give him the strength and motivation to keep going and find a way to escape or at least endure.
He could rely on his natural demigod abilities. His control over water, for instance, might help him find sources of water in Tartarus that are safe to drink or use for protection. Also, his combat skills, which he has honed over many battles, would be crucial in fending off the various monsters in Tartarus.
Well, one reason could be that he's wrongly accused of a major crime against the gods. Maybe some false evidence is planted, making the gods believe he's a threat, so they banish him. Another reason might be that he's trying to protect someone or something, and his actions are misinterpreted as going against the gods' will. For example, if he's trying to save a powerful but 'forbidden' creature, the gods might see this as a violation and send him to Tartarus.
They might survive by relying on their combat skills. Percy, with his sword - fighting abilities and Zoe's archery skills, can fend off the various monsters in Tartarus. Also, they could use the environment to their advantage. For example, hiding in the dark corners or using the natural formations as shelters.
He might use his sword skills and his ability to control water. For example, he could create shields out of water to protect himself from attacks. He would also try to find any weaknesses in his enemies. If there are any water sources in Tartarus, he could use them to his advantage, like making geysers to distract or attack his foes.
In the fanfiction, if Percy gets banished to Tartarus, he could potentially meet some old enemies who have been banished there too. Maybe he'd have to team up with some unlikely allies to find a way out. It would be a struggle for him, as Tartarus is a place where hope is almost non - existent. He'd also have to deal with the harsh environment, like the rivers of fire and the jagged rocks.
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.
Perhaps a prophecy misinterpretation. If a prophecy was misread and it seemed like Percy was the cause of great evil to come, the gods might take drastic action. For instance, if the prophecy spoke of a 'child of the sea' causing destruction, and they wrongly assumed it was Percy without fully understanding the context.