The Joker is one of the darkest villains to ever exist, and he's no stranger to teaming up with other villains at times, but even Joker loses his temper at other evil-doers when they harm Robin. The villain Black Mask found this out the hard way when he killed Batman's fourth Robin, Stephanie Brown.
Few comic book characters have dealt as much damage to their opposing hero as the Joker. From cutting off Alfred's hand, shooting Barbara Gordon in the spine, torturing James Gordon, and beating Jason Todd to death the Joker has proven to be an absolute menace to the Batfamily and their allies at large. Joker hasn't ever really interfered with any other villains in their attempts to kill Batman, he never seemed to care when Bane broke the Bat, or even when Riddler tries to outsmart Batman once again. Joker has always let the other villains have their turns... that is until Black Mask took things too far.
In Detective Comics #810 by Andersen Gabrych and Pete Woods, readers see Black Mask after the events of Wargames, fighting Batman. As Black Mask attempts to escape The Dark Knight, he is captured by none other than the Joker. Black Mask and Joker struggle for a while with Joker eventually winning, thanks to him bringing a gun to a fistfight. Black Mask is completely surprised that Joker is attacking him, not even knowing why, until Joker so kindly informs him. In Joker's own words, "Oh, Blackie McMaskie, Everyone knows my favorite job in the whole wide world is killing Robin."
One of the Joker's crowning achievements in comic history, even bigger than the infamous Killing Joke is what he did to Jason Todd. Joker is the only Batman villain to have actually kept a Robin dead for a significant period of time. While other villains have technically killed Robins as well, it was only for a few seconds or by a fairly unimportant villain, as is the case with Heretic and Damian Wayne. Joker is the only one who killed a Robin and had it really matter. Jason Todd was dead for 17 real-world years, that is a huge accomplishment for Joker in a medium where death hardly ever matters. Black Mask beat Stephanie Brown to death, she wasn't Robin for long, but she was one. While this was eventually retconned, at the time, both readers and the Joker believed that Black Mask had truly killed a Robin. Joker conveyed his rage when he told Black Mask, "You ruined my life when you killed Stephanie Brown, the sweetest little Robin one could ever hope for! Don't you know that's my job?"
Black Mask has been a pain in Bruce's life for a while, his manipulations during the Wargames story arc caused havoc throughout Gotham and lead to the deaths of two of Batman's trusted teammates. Black Mask was clearly fine with making enemies of the Batfamily when he killed Robin, what he clearly didn't expect though was making an enemy of The Joker.