Well, I'm not sure which specific 'amy sonic love story' you mean. There could be many fictional stories involving characters named Amy and Sonic. Maybe it's a story created by a fan where Amy has a crush on Sonic and they go on adventures together, with Amy constantly trying to get Sonic's attention while Sonic is more focused on saving the world.
Sonic and Amy's relationship is quite interesting. Amy has a huge crush on Sonic. She is always chasing after him, her love being very passionate. Sonic, on the other hand, while he may not always show it in the most obvious way, he does care about Amy. In their adventures together, there are moments where Sonic's protective side for Amy shines through, which could be seen as a sign of his underlying feelings. Their love story is one of the unspoken yet deep - rooted emotions in the Sonic universe.
There are many interesting fanfictions about Sonic and Amy's love. Some focus on their adventures together where their love slowly blossoms. For example, in some stories, they might face a powerful enemy together and through that experience, their bond deepens.
It's hard to say whether the 'amy kills sonic fanfic' is popular. The Sonic fanfic community is diverse, with fans having different tastes. Some might enjoy exploring the darker and more controversial storylines like this one, but it could also be that a large portion of the community prefers the more traditional, positive stories. So it might not be as mainstream popular as some of the more typical Sonic fanfics.
One key element is Amy's love for Sonic. It drives her actions and her attempts to be close to him. Another is Sonic's somewhat aloof nature in response to her love, which creates tension. And of course, the adventures they go on together, which could be seen as a backdrop for their relationship to develop.
There is no official story about Dark Sonic and Amy being in love. Dark Sonic is a more aggressive and chaotic form, and Amy is usually associated with Sonic in the normal Sonic series. Their personalities and the nature of Dark Sonic make it an unlikely pairing in the canon.
Amy Rose shows her love by constantly chasing Sonic. She is always by his side during his adventures, ready to help. For example, she'll bring him a meal or offer to patch up his wounds.
Tails could be one of the main characters. He might play a role in helping Amy realize that her chasing Sonic isn't healthy. For instance, he could give her advice based on his own observations.
For Amy, she could become more understanding of the 'evil' or opposing side. Instead of just seeing Metal Sonic as a bad guy, she might learn to look deeper into his existence as a creation. This could make her more empathetic in general.
In the Sonic universe, Sonic and Amy have a somewhat established relationship dynamic, with Amy chasing Sonic's affection. Dark Sonic, being a transformation of Sonic, is not really in the picture when it comes to love in the official story. But if we were to create a fictional love story for them, it could start with Amy's curiosity about this darker side of Sonic. She might try to reach out to Dark Sonic, believing she can bring out the good in him. Dark Sonic, at first, might not understand her intentions but gradually could develop feelings for her as she shows him kindness and acceptance in a world that usually fears his power.