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.
Robin could try to form an alliance with someone within Deathstroke's organization. There might be a disgruntled henchman or someone who has a change of heart. Robin could convince this person to help him escape by appealing to their sense of morality or by offering them something in return, like protection from Deathstroke's wrath once he discovers the escape.
One possible plot twist could be that Robin has been secretly trained in a new combat technique that he uses to outwit Deathstroke when Deathstroke least expects it. Maybe he pretends to be more injured or helpless than he really is, and then strikes back at a crucial moment.
One possible fanfiction plot could be that Deathstroke kidnaps Robin to use him as bait for Batman. He wants to lure Batman into a trap and finally defeat him. Robin, being the resourceful sidekick, leaves behind small clues for Batman to find him, adding an element of mystery and suspense to the story.
To create a believable relationship, start with their fundamental differences. Robin is a hero, and Deathstroke is a villain. They could be initially at odds, constantly trying to outwit each other. But then, introduce some common ground, like a shared enemy or a mutual respect for each other's combat skills. This can slowly build a complex relationship.
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.
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.
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 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.
One idea could be that Poison Ivy kidnaps Robin to use him as a bargaining chip against Batman. Maybe she wants Batman to stop interfering in her environmental plans. So she holds Robin in her lair, which is filled with all kinds of dangerous plants.
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.