Yes, there are some out there. One popular one might be on Archive of Our Own. It often delves into their relationship, exploring how Percy, as Achilles' brother, might interact within the world of Greek mythology. It could show them training together, facing challenges side by side, and how Percy might deal with the legacy of having such a famous brother like Achilles.
Well, the plot could involve Percy being in the shadow of Achilles at first. Since Achilles is so well - known in Greek mythology. But then, a great danger arises that only the combined powers and skills of both of them can overcome. They have to journey to the Underworld to stop a dark force from escaping. During this journey, they reconcile their differences and strengthen their brotherly bond as they face the terrors of the Underworld.
One possible plot could be Percy discovering his connection to Achilles while on a new quest. Maybe he has to face a powerful enemy that only his newfound link to Achilles can help him defeat. For example, he might gain some of Achilles' combat skills or invulnerability in certain situations.
Percy might become more confident in his abilities. Knowing he is related to Achilles, a great hero, could give him a boost. He may also become more strategic in combat, learning from Achilles' military tactics.
In the fanfiction of the Curse of Achilles in Percy Jackson, many authors like to play with the idea of Percy's vulnerability. Even though he has the curse which makes him almost invincible, there are always ways around it that the fanfic writers come up with. This could be related to his emotional state or some hidden loopholes in the magic of the curse.
One common theme is power and its consequences. The Curse of Achilles gives Percy great power, but it also comes with risks. Another theme is heroism. Percy has to be a hero while dealing with the limitations and advantages of the curse.
One common theme is the idea of heroism. Percy, being a hero himself, is on a mission to save Achilles. This often involves him facing various challenges and obstacles, showing his courage. Another theme could be friendship. As Percy tries to save Achilles, a bond might form between them, or it could be about Percy upholding a pre - existing friendship.
Another theme is identity. With the curse, Percy is somewhat changed. He's no longer just the regular demigod. Fanfiction may delve into how he reconciles this new, more powerful self with his old identity. For instance, he might struggle with the idea that he's now a 'super' demigod while still wanting to be seen as the same Percy by his friends. This can lead to a lot of internal conflict within the character in the fanfiction.
There could also be antagonists. For instance, some old enemies of Percy might be drawn to him because of the Curse of Achilles. They might see it as a challenge or an opportunity to finally defeat him, and these antagonists would be important characters in driving the story forward.
I'm not sure of specific 'Percy Saves Achilles' fanfiction titles off the top of my head. However, you can join relevant fan communities on platforms like Reddit or Tumblr. Fans in these communities often share and recommend great fanfics. They might be able to point you to some really good 'Percy Saves Achilles' stories.