Amy Rose has a deep affection for Sonic, not Shadow. So in the official Sonic lore, there is no such love story between Amy Rose and Shadow. However, if we were to imagine it, perhaps they could meet during a fight against a common enemy. Shadow, initially cold and distant, might be gradually warmed by Amy's persistent kindness and her strong will. And Amy might be attracted to Shadow's mysterious and powerful nature.
One possible challenge could be their different personalities. Amy is outgoing and affectionate while Shadow is more reserved. This could lead to misunderstandings in their communication. Another challenge might be their different goals. Amy is often focused on Sonic or helping others in a more direct way, while Shadow has his own complex motives related to his past. Also, the public perception in the Sonic world could be a problem. Since Amy was known for her love for Sonic, others might be skeptical or even against her relationship with Shadow.
You can try fanfiction.net. It has a large collection of fanfics from various fandoms, and there's a good chance you'll find some amy rose shadow fanfic there.
One good amy rose shadow fanfic could be 'The Adventures of Amy and Shadow'. It might involve their adventures in a magical world where they team up to defeat an evil force. In this fanfic, their unique personalities would shine through as they face various challenges together.
One common theme is family. Since there's a baby involved, it often explores how Amy, Shadow, and the baby form a family unit. Another theme could be protection. They usually have to protect the baby from various threats.
One popular storyline is about Amy trying to get Shadow to open up more. Since Shadow is often brooding and reserved, Amy's cheery and persistent nature can lead to some interesting interactions. For example, she might drag him into various adventures where he slowly starts to show his softer side.
A lot of 'Shadow the Hedgehog x Amy Rose fanfiction' has the theme of forbidden love. Since they are from different backgrounds in the Sonic universe, their relationship might be seen as something that goes against the norm. This adds an element of drama and tension to the stories. Also, the theme of self - discovery is present. As they get closer, both Shadow and Amy might discover new sides of themselves.
One interesting aspect is how her darker personality can contrast with Shadow's own brooding nature. In fanfiction, this can lead to some really intense and unique interactions. For example, they might be drawn to each other because of their shared sense of being different from the norm in the Sonic universe. And Dark Amy Rose might be portrayed as having powers or abilities that are enhanced or different from the original Amy, which makes her role in the story with Shadow all the more exciting.
One idea could be that Amy Rose gets lost in a mysterious forest and Shadow Lemon has to find her. Along the way, they face various challenges that make them rely on each other and in the end, they form a deep friendship.
Another way is through misunderstandings at first. Let's say Shadow Lemon accidentally breaks something that is important to Amy Rose. Amy Rose gets angry, but then they both realize it was a misunderstanding. This kind of situation can lead to better communication and understanding between them later on.