Perhaps some remnants of Homeworld's military that still hold a grudge against the Crystal Gems. They might think that by kidnapping Amethyst, they can force the Gems to stop their activities on Earth or give up some valuable information.
There's also a possibility that it's a new villain created specifically for the fanfiction. This villain could be after Amethyst's unique powers, thinking that they can use her shape - shifting abilities for their own evil plans.
Another option is that it's a human who has somehow discovered the existence of Amethyst and the other Gems. This human could be a mad scientist type who wants to study Amethyst's unique gemstone and abilities. He or she might not understand the full implications of what they're doing and just see Amethyst as an interesting specimen to experiment on.
Well, in such a fanfiction, the other characters like Steven and the Crystal Gems would likely go on a rescue mission. They'd use their powers to track her down. Steven might use his shield to protect them during the search, and Pearl could use her spear skills. Garnet would probably be leading the way with her future vision to find Amethyst as quickly as possible.
Well, in such a fanfiction, the other Crystal Gems might go on a frantic search for Amethyst. They could face many challenges along the way, like dealing with new enemies or having to make difficult choices to get her back.
It could be an enemy from one of his past cases. Someone who holds a grudge against L for getting them caught or ruining their plans before.
It could be a rival guild member who wants to use Juvia as leverage against Fairy Tail. Maybe someone jealous of her powers or her relationship with Gray.
In some 'damian gets kidnapped fanfiction', the kidnapper could be an otherworldly being. Let's say an alien or a magical creature that has an interest in Damian for some strange reason. It could be that Damian has a unique energy or power that the otherworldly being wants to study or harness. Or perhaps it's a human who has been corrupted by some dark magic or technology and is acting on behalf of a more powerful, hidden force that wants Damian for its own nefarious purposes.
Maybe it's a group of poachers who are after rare Pokémon. Gengar, being a relatively unique and powerful ghost - type, would be a valuable catch for them. They could plan to sell Gengar on the black market for a high price.
It could be Shredder. He's always been after the turtles.
It could be a rival spy agency. They might see Moneypenny as a valuable target to get information about MI6's operations. They would likely be highly trained and well - equipped.
Maybe it's a character from one of the games Matpat has theorized about. For example, if he made a theory about a game villain being more complex than thought, that villain could come to life in the fanfiction and kidnap him to prove his own power and intelligence.