Jason Todd (Under the Red Hood)

Jason Todd is the main antagonist in Batman: Under the Red Hood. In this animated film he is a vigilante who is at odds with Batman due to killing - an act Batman flat out refuses to do despite Joker's absolute joy at how he broke Todd and made him a killer. The animated feature is basically a retelling of the comic book arc but has a few differences, as can be expected due to the difference in media.

Past
Before meeting Batman, Jason Todd was a kid criminal, having been arrested at least once. Batman met the boy in Crime Alley, where Jason had just finished removing the tires of the Batmobile as an act of vandalism. Instead of calling the authorities, however, Batman, impressed with the boy and also believing he needed to curb his criminal tendencies, took him in as the second Robin, after Dick Grayson left and made a name for himself as Nightwing.

During one of their first missions, Jason Todd proceeded to aid Batman in taking down the Riddler while the latter was conducting a heist on a museum, also proceeding to supply a "riddle" before taking him down by kicking him in the crotch.

As he grew older, however, his personality turned far darker, becoming very cocky and virtually merciless, with him once ruining an operation because, when taking down a drug-dealing pimp, he broke the man's collarbone just enough to put him into shock, which resulted in a stern telling off from Batman due to his needing him for interrogation.

Death
Eventually, Jason Todd and Batman uncovered a crime spree occurring in Bosnia, where the Joker had poisoned an entire hospital and was raiding medicine (in reality a diversion to ensure Ra's al Ghul and his League of Shadows toppled the European Economy). However, Jason Todd's recklessness got the better of him and proceeded to chase after the Joker, which resulted in his capture. Held prisoner by the Joker, he was subject to torture via repeated beatings from a crowbar by the deranged clown, and then left to be blown up by the bomb, which went off just as Batman arrived to rescue him. The explosions ultimately killed him.

Revival
However, his body never returned to Gotham: Ra's al Ghul, out of guilt for his unintended role in Jason Todd's death, secretly replaced his corpse with a realistic dummy, and proceeded to use the Lazarus Pit to resurrect him to repair the damage. Unfortunately for Ra's al Ghul, this had disastrous side effects: While Jason Todd's body was resurrected, his mind was left damaged. He then proceeded to escape custody of the League of Shadows, narrowly survived falling into the nearby river from a high drop, and somehow managed to find his way back to Gotham five years later.

Seeking Vengeance
Learning that Batman failed to avenge his death at the hands of the Joker, Jason Todd was enraged, and proceeded to adopt the former identity of the Joker, the Red Hood, and proceeded to take control of the various drug dealers under the employ of Black Mask, allowing them to continue dealing on the streets under the condition that they pay 60% of the shares to him, and they stay away from children when dealing drugs, threatening to kill them should they disobey (also producing a duffel bag containing the decapitated heads of their various lieutenants that he allegedly did in under two hours to make clear that his threat was genuine). In addition, he also had Amazo stolen by various hired crooks, although after Batman busted the heist as well as destroyed the Amazo with Dick Grayson, Red Hood proceeded to kill them with sniper rounds. He then escaped via a blue convertible, and managed to lure Batman to the ACE Chemical Plant, where Joker was created. He then reminded Batman that it was his first mistake, possibly even his worst one. He then fled after a brief exchange, also shooting the leaking fuel from the car to destroy the plant to ensure Batman is unable to pursue him.

Meanwhile, he then proceeded to steal another arms shipment from Black Mask (having overheard him via a planted bug), and after Batman interfered, Red Hood proceeded to drop the chopper over the edge, as well as enter a chase by the Dark Knight and Nightwing, eventually escaping at the train station via an explosive and under the cover of a passing train, although not before telling Batman that he hadn't lost his touch while also dropping the name "Bruce" as a hint for the Dark Knight towards his potential true identity. He then proceeded to fight the Fearsome Hand of Four mercenary group, also calling in Batman earlier for aid, eventually managing to knock out three of the mercenaries while killing the fourth. They then proceeded to get into an argument about how to deal justice before taking his leave with a smoke grenade. He then proceeded to use a rocket launcher at Black Mask's office, thus forcing the crime lord to arrange for the Joker's release.

Red Hood then arrived at the area Joker was at, revealing he had in fact intended all along for Black Mask to release Joker, as he wanted to have revenge against him. After Batman prevented Joker from torching the various drug dealers, Red Hood proceeded to abduct Joker before Batman had a chance to retrieve him, and also left a message telling the Dark Knight (who now knows his identity as Jason Todd and how he was revived) that he has Joker and that he meet him in crime alley if he wants Joker. He then goes to an abandoned apartment building and proceeded to dish out his revenge against the Joker by beating him with a crowbar, just as Joker himself did to him five years earlier.

He then encountered Batman in Crime Alley, and after fighting him all the way to the apartment complex, Jason Todd proceeded to rant that Batman should have killed the Joker after not only his murder of him, but also all of the carnage he's caused in general. After learning his old mentor would not break his one rule and why, he then tries to force him to shoot him or let him shoot the Joker. However, Batman refused, and eventually used a batarang to block out the barrel of his gun, detonating it in his hand after he attempted to shoot him in order to force him to act. Jason Todd then proceeded to set off explosives he had presumably placed in the apartment earlier, although he slumped down when Joker interfered with Batman's attempt to disarm the bombs, although he was nonetheless saved by Batman at the last second. However, he disappeared afterwards.