It could be Nightwing. He was once Robin himself and has a special connection to the current Robin. Nightwing might hear about the kidnapping and step in to save Robin, using his own unique fighting style and experience.
The other Teen Titans could also play a big role in the rescue. Starfire could use her powers to fly in and distract Slade while Cyborg and Beast Boy create a diversion. Raven could use her magic to break any spells or traps that Slade has set for Robin. They would all work together as a team to get Robin back safely.
One possible plot for this fanfiction could be that Bane kidnaps Robin as part of a revenge plot against Batman. Robin is trapped in a dangerous situation, and he has to rely on his training and his mental strength to survive. Bane might taunt Batman with messages about Robin's kidnapping. As Batman races to save Robin, Robin also tries to find a way to free himself and help Batman in the process. The story could explore Robin's growth as a character while facing this difficult situation and the complex relationship between Batman, Robin, and Bane.
Robin would probably be both scared and angry. He's a brave kid, but facing the Joker alone is no small feat. He might initially try to fight back if he has the chance.
His friends like Batman and Nightwing could be main characters. Batman might use his detective skills to figure out what's wrong with Robin, and Nightwing could be there to offer emotional support.
Robin would probably stay calm and observant. He's been trained well, so he'd immediately start looking for any weaknesses in his captivity situation. He might try to pick the locks on his restraints if he's bound, or find a way to communicate with his team secretly if there's a chance.
Robin could use his intelligence to analyze Deathstroke's lair and find a weakness in its security system. He might notice a pattern in the guards' patrols or a flaw in the locking mechanisms. Then, he could use his acrobatic skills to create a distraction and slip away unnoticed.
It could be the Joker. He's always up to no good and kidnapping Robin would be a great way to mess with Batman. The Joker might want to use Robin to force Batman into a series of cruel and twisted games.
Villains from the Batman rogues' gallery are likely kidnappers. For instance, the Riddler might kidnap Red Robin to challenge Batman to solve his riddles to get him back. Another one could be the Penguin. He might see Red Robin as a valuable hostage to bargain with for more power or money in Gotham's underworld. Black Mask is also a possibility. He's always looking for ways to gain an edge over the other criminals and having Red Robin as a captive could be part of his scheme.
Robin might initially be defiant. He's a trained fighter and detective, so he'd likely try to gather as much information as he can about his surroundings. He could be looking for any weaknesses in Lex Luthor's security setup or trying to figure out what Luthor's endgame is.
In the world of fanfiction, there are often hidden gems. For 'Robin kidnapped' fanfictions, you might find good writers by looking at the reviews and ratings of stories with this plot. Writers who get a lot of positive feedback for their take on this theme are likely to be good. They may be skilled at character development, making the story of Robin's kidnapping and possible rescue really engaging.