While Dick Grayson is one of the greatest heroes in the main DC Universe, The Dark Knight Returns universe saw Robin fall into the darkest pits of evil by becoming the newest version of the Joker.
Frank Miller, Klaus Janson and Lynn Varley's iconic The Dark Knight Returns cemented many of the ideas that define Batman today in comics and beyond. The series saw a retired Batman return to crime-fighting after seeing the world descend into crime and ends with him facing off against Superman, who's now a pawn of the U.S. government. Taking place five in-universe years later, Miller and Varley's The Dark Knight Strikes Again would see Batman facing up against a new villain that was eventually revealed to be a crazed Dick Grayson, having taken up the mantle of Joker after being fired as Robing and descending into madness.
Throughout The Dark Knight Returns, Batman recruited Carrie Kelley as the new Robin with nary a mention of Grayson. In The Dark Knight Strikes Again, after training an army of "Batboys" to fight Lex Luthor's police state, Batman and Kelley started raiding government facilities to free captured superheroes from their imprisonment. The Question, working separately from Batman, went to get help from an aged and nearly powerless Martian Manhunter. They were attacked by a mysterious man who resembled the Joker. He killed Martian Manhunter while Question managed to escape thanks to Oliver Queen's help. Afterward, the new Joker continued killing heroes, stealing their costumes then wearing them when he killed other heroes.
Dressed in a Robin costume, the new Joker attacked Carrie Kelley in the Gotham catacombs. Using Oliver Queen's equipment, she killed him and took him apart piece by piece. Thinking she was safe, Kelley continued life as usual only for the Joker lookalike to attack her in the Batcave. Batman rushed to her aid and recognized him as Dick Grayson, his former Robin who he had fired decades earlier. Grayson revealed he had undergone radical gene therapy that had given him the ability to shapeshift and regenerate his body. Batman and Grayson went on to battle through the Batcave with Batman even beheading him at one point, only for Grayson to reattach his head. Eventually, Batman pushed Robin through a trapdoor into the lava below, content that they'd die together only to be saved by Superman at the last second.
Canonically, The Dark Knight Returns and The Dark Knight Strikes Again are preceded by Miller and Jim Lee's All Star Batman and Robin, the Boy Wonder, which was released between 2005 and 2008. This series depicts how Dick Grayson became Robin in the TDKR universe, and it also details the abuse Robin received at the hands of Batman that eventually led him down the path to becoming the new Joker. In All Star Batman and Robin, Batman is significantly more sadistic and comfortable with violence than many other incarnations. This predilection for violence naturally rubbed off on Robin, who Batman basically kidnapped drafted into his war on crime after finding him crying at his parents' grave after they were killed by the Joker's hitman. Batman intentionally torments Robin throughout his training, forcing him to hunt rats in the Batcave for food and habitually beating him if he didn't follow his orders to the letter. At one point, Robin almost killed Green Lantern, and he would have died if Batman didn't perform an emergency tracheotomy. This interaction shows this Dick Grayson's natural inclination towards violence, foreshadowing his descent into evil in The Dark Knight Strikes Again.
While Grayson's time with Batman clearly affected his life for the worse, Carrie Kelley seemingly grew up to be a more well-adjusted superhero in The Dark Knight III: The Master Race. But clearly, Dick Grayson's abuse at the hands of Batman dramatically affected him, causing him to go down a dark path and become the Joker.