The Joker took the lives of the first Robin and Batgirl in his most disgusting crime, slaughtering the young heroes in front of Batman and pushing the Dark Knight to finally break his "no kill" rule and take his nemesis' life. While Joker famously killed the second Robin, Jason Todd, in Batman: Death in the Family, his attack on Dick Grayson and Barbara Gordon was even more horrific, scarring Batman on a fundamental level and pushing him to do the unthinkable.
The horrific attack took place in JLA: The Nail - an Elseworlds story set in an alternate universe with just one difference to the mainstream: an errant nail popped the tire of Jonathan and Martha Kent the night they would otherwise have discovered the infant Superman's escape craft. Because of that small change, the history of the DC Universe unfurls very differently, with the Justice League of America struggling with outsized threats, and an unchecked Lex Luthor waging a campaign to turn the public against metahumans with help from a tragically corrupted Jimmy Olson.
The main difference Batman experiences in the reality of The Nail is that he's even more closed-off from his JLA colleagues, never coaxed out of his dark, brooding nature by Superman's friendship. When Joker attacks Arkham Asylum with advanced "power sleeves," Batman turns down his Justice League colleagues' help and goes to the scene, insisting that Robin and Batgirl stay outside the force bubble thrown up by Joker - a bubble which suspiciously allows Batman's allies entry to the crime scene. When Batman confronts Joker, he's easily bested by the villain's new technology, and is horrified to realize that a young Dick Grayson and Barbara Gordon have disobeyed his orders. Gleeful at having a way to torture Batman, Joker forces his eyes open and begins an "anatomy lesson," torturing the young heroes while declaring, "I want my pound of flesh... Whoops! That looks more like a pound and a half."
It's a genuinely distressing scene, heightened both by the obvious youth of Batman's wards - Catwoman describes them as "children" - and by the visceral (though unseen) nature of the attack, with the story cutting away from Joker's glee and back again to imply a process more horrifying and prolonged than the beating suffered by Jason Todd. Batman's wards plead for him to help, and the Dark Knight begs Joker to stop, shedding a tear as he's forced to watch what's easily Joker's darkest comic crime to date. Catwoman is eventually able to rescue Batman, who snaps and kills Joker in front of the press, but the damage is done, and both Robin and Batgirl perish.
It's eventually revealed that a deranged Jimmy Olson gave Joker his new tech in an attempt to turn public sentiment against heroes, and while he's ultimately stopped by Superman - who it's revealed was found and raised by an Amish community - Batman still leaves the Justice League of America in disgrace, hoping to protect them from guilt by association. Catwoman joins Batman as Batwoman, an adult ally in the war against crime, and Batman later gets some closure in the sequel JLA: Another Nail, from the same team of Alan Davis and Mark Farmer. Here, Batman faces Joker's spirit, attempting to finally drag the villain to Hell, but is saved at the last moment by the souls of his murdered wards, finally rejoining the Justice League soon after.
Joker has appeared in countless variations and in different types of media, sometimes as a harmless supervillain and sometimes as a brutal serial killer, but in few places is the sadistic glee that defines the character more potent than JLA: The Nail. Davis and Farmer's juxtaposition of Robin and Batgirl's gee-whiz innocence with Joker's shocking violence creates one of Batman's darkest moment ever, and one which - thanks to DC's Infinite Frontier bringing past stories and Elseworlds narratives back into the continuity of DC's multiverse - may be newly relevant to the Dark Knight's ongoing stories.