One common theme is physical injury during battles. Given Levi's role as a strong fighter in AOT, fanfictions often explore scenarios where he gets seriously injured in combat, like being wounded by Titans or in fights with other humans. This could lead to his comrades having to take care of him, creating moments of vulnerability and bonding.
You can start by looking on fanfiction platforms like Archive of Our Own (AO3). It has a large collection of Attack on Titan fanfictions, including ones about Levi being hurt. Just use the search function and type in relevant keywords like 'Levi hurt' to narrow down your search.
One great AOT female Levi fanfic is 'The Captain's Heart'. It delves into a unique story where a female character has an interesting relationship with Levi. The writing is engaging, and it really captures the essence of the Attack on Titan world while exploring a different side of Levi's character.
The theme of hope in the face of adversity is also present. Despite Levi getting hurt, the fanfiction may show how the characters around him and he himself still hold on to hope for recovery and victory in the long run.
One common theme is physical injury. Writers often depict Levi getting hurt during battles, which shows his vulnerability despite his tough exterior. For example, he might get seriously wounded in a fight against Titans and have to struggle to recover.
AOT has a huge fan base, and many female fans like to project themselves or create their own characters in the universe. Fanfics about a female and Levi allow them to do that. It also gives an opportunity to explore different aspects of the AOT world that the original series might not have fully covered, like how a female character might interact with Levi in a more personal way.