Maybe a rogue mutant. There are all kinds of mutants in the TMNT universe. One that has a grudge against the Turtles or just wants to use Donatello's skills for their own gain could be the kidnapper.
Another possibility is a human scientist who has gone mad with power. He might have been studying the Turtles from afar and decided that Donatello's technological know - how could help him achieve his insane goals. So he devises a plan to kidnap Donatello and force him to work for him.
It could be the Foot Clan. They've always been enemies of the Turtles, and kidnapping Mikey would be a way to get back at them or gain some advantage.
Well, perhaps a new villain who has heard of Donatello's genius kidnaps him to use his brainpower for some evil scheme in the underworld. Donatello might be able to use his wits while in captivity to leave clues for his brothers. And his brothers, once they realize he's missing, would start scouring the city, interrogating informants and following leads to find him.
It could be Shredder. He's always been after the turtles.
It could be a secret society that has been observing their actions and sees them as a threat to their hidden agendas. This society might have members with special skills and resources to carry out the kidnapping.
Maybe it's a group of villains working together. They could be from different factions but united by the idea that Izuku has the potential to become a huge threat to their plans. They might kidnap him to either eliminate him or turn him to their side. Also, it could be a lone, obsessed fan of a villain who wants to prove themselves by bringing Izuku to their idol.
A group of outcasts from different islands might kidnap Moana. They feel that they have been wronged by the 'normal' society that Moana represents. They hope that by kidnapping her, they can get the attention they deserve and force the islands to change their ways. But Moana listens to their grievances and tries to find a way to help them while also finding a way home.
It could be Zeref. Since Zeref has an interest in powerful magic users and Natsu is a strong dragon slayer, Zeref might kidnap Natsu to study his magic or use him in some dark plan related to his quest for immortality or power.
It could be a jealous rival from his own village. Maybe someone who is envious of Shikadai's natural talents and popularity, so they decide to kidnap him to get him out of the way.
It could be an envious rival. Maybe someone who's always been in the shadow of Osomatsu and his brothers and decides to take matters into their own hands by kidnapping Osomatsu. Another option is a deranged collector. This person might see Osomatsu as a rare item to add to their collection of oddities. Or it could be a vengeful spirit. In a more supernatural setting, a spirit with a grudge against the Matsuno family could kidnap Osomatsu as a form of revenge.
It could be a rogue werewolf. Maybe this werewolf has a grudge against Stiles' pack and thinks that by kidnapping Stiles, he can get some sort of revenge or leverage.