Survival is a big one. Tartarus is a very hostile place, so Percy has to fight to stay alive. Another theme is redemption in some cases, like if he feels responsible for getting thrown in there.
One possible plotline could be Percy's struggle for survival in Tartarus. He might have to face off against various terrifying monsters. Another could be his journey to find a way out while dealing with the psychological trauma of being in such a hellish place. And perhaps he discovers some long - hidden secrets about Tartarus itself during his time there.
His friends like Annabeth or Grover could be the ones to rescue him. They might discover a way into Tartarus and brave all the dangers to get to Percy.
One possible plot could be Percy's struggle to survive in Tartarus. He might have to face the various terrifying monsters there, like the giants or the powerful demons. Maybe he'd find some unexpected allies among the damned souls, and together they'd try to find a way out.
One popular 'percy thrown in tartarus fanfiction' is 'Into the Abyss'. It really delves into Percy's struggles and his attempts to survive in Tartarus. The author does a great job of describing the terrifying environment.
The Titans that were banished to Tartarus could be major antagonists. They might see Percy as an intruder and a threat, and try to stop him from escaping or even try to use him for their own purposes. Also, the various monstrous creatures native to Tartarus, like the Empousai or the Arai, could constantly be attacking Percy.
A third plotline could be Percy's search for a powerful artifact or knowledge in Tartarus that could help him in his future battles or save his friends. Along the way, he discovers secrets about the origin of the gods or the true nature of Tartarus itself, which changes his understanding of the world he thought he knew.
The theme of self - discovery is quite prevalent. After Tartarus, Percy may start to question who he is and what his purpose is. He has faced such extreme situations that it makes him reevaluate himself. Also, the theme of power and its limits is often explored. He might have gained new powers or a new understanding of his existing powers during his time in Tartarus, and fanfictions play around with how he uses or controls them.
Survival is a big one. Tartarus is such a harsh and dangerous place, so Percy has to find ways to stay alive. Another theme is self - discovery. Facing the extreme challenges there makes Percy learn more about his own strength and limitations.
The Titans or Giants that were banished to Tartarus could be the main antagonists. They might see Percy as a threat or an opportunity to escape and seek revenge on the Olympians.
One common theme is identity struggle. Percy has to figure out who he is now that his parentage has changed. He was known as a son of Poseidon, and suddenly being the son of Tartarus throws his whole self - concept into chaos.