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.
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.
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.
Another theme is mutual understanding. Despite their different personalities, they seem to understand each other on a level that others don't. Fanfics often play on this, showing how they can communicate without words at times. For example, in some stories, Levi can tell when Hanji is about to do something reckless just by a look in her eyes. And Hanji can sense when Levi is more stressed than usual. This mutual understanding forms the basis of many emotional and plot - driving moments in the fanfics.
One common theme is loss. Given the brutal world of Attack on Titan, Levi might cry over the loss of his comrades. His close relationships with his squad members make their deaths a heavy blow.
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.