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.
In the fanfiction, the environment of Tartarus itself could be considered an antagonist. The extreme heat, the toxic gases, and the ever - present danger of falling into bottomless pits. And on top of that, there could be some sort of demon - like creatures that are specifically created or summoned to hunt down Percy and Zoe and prevent them from achieving their goals.
Well, one possible plot could be that Percy and Zoe have to face various ancient and terrifying monsters in Tartarus. They might encounter challenges that test their friendship and their individual strengths. For example, they could come across the Titans that were once banished there, and have to find a way to avoid or defeat them while also trying to find a way back to the upper world.
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 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.
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.
A third plotline could be about Percy's mental and emotional state during his banishment. He could be dealing with feelings of betrayal, as he was banished. He might question his identity and purpose, and throughout the fanfiction, he gradually overcomes these doubts and insecurities, emerging stronger in character even if he's still trapped in Tartarus.
The monsters native to Tartarus could also be antagonists. These could be huge, grotesque creatures that have never seen the outside world. They might attack Percy on sight, seeing him as prey. Some of them could be powerful enough to even give Percy a hard time, especially if his powers are weakened in 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.
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.