Two-Face's early history mirrors his mainstream counterpart in many ways; he served as the District Attorney of Gotham City for some time, working with Batman and Commissioner Gordon, before Batman vanished from Gotham. At some point, a gangster threw a vial of acid in his face and badly disfigured him, ending his career as the D.A.'s office suggested he step aside for a more 'visually appealing' candidate given the scale of the damage done to his face.
Some time after the now-vampiric Batman was staked and "killed" by Alfred and Gordon after he killed the Joker, Dent was recovering in the hospital from his disfigurement. When the doctor removed his bandages and began to discuss the possibilities of reconstructive surgery, Dent suddenly became violent, assaulting the doctor and declaring that "if the law doesn't want me, maybe the other side does!" Subsequently, Dent stored out and began a life of crime as Two-Face, running rampant throughout Gotham along with many other villains, sending his former ally Gordon a note announcing that everyone would 'pay double'. At some point, he formed a small gang of criminals, which included Killer Croc as his muscle.
Faced with the massive crime wave of Gotham's villains, Alfred bought Batman back to life by removing the stake in an act of desperation, only for Batman, now a slave to his vampire instincts after drinking the Joker's blood and his months of decay in the crypt, to embark on a violent rampage, draining his enemies of their blood and beheading them to prevent them from returning as vampires themselves.
After the deaths of the Penguin, the Riddler, and the Scarecrow, Two-Face and Killer Croc met with their gang to discuss how to stop Batman. By flipping his coin, Two-Face decided to form an alliance with "their opposites"- Alfred and Commissioner Gordon, the only two people remotely qualified to oppose what Batman had become.
Alliance of Opposites
Meeting with Gordon and Alfred on top of the police station- shortly after Batman had killed Poison Ivy and left her head outside the GCPD- Two-Face proposed that they join forces to stop Batman, but Gordon refused to work with criminals like him. Accepting their refusal, Two-Face departed with Croc, stating he would give Gordon time to decide.
Eventually, Batman slaughtered the Black Mask gang and leaves their heads on the fences of Blackgate Penitentiary as a warning to the inmates within before proceeding to kill all the homicidal inmates within Arkham Asylum, leaving Two-Face, Killer Croc, and their gang the only remaining villains in Gotham. With this brutal assault, Gordon was forced to accept Two-Face's offer.
Clash in the Batcave
Tracking Batman down to his new lair in the remnants of the Batcave, the group devised a plan: Alfred would lure Batman into the center of the cave, where Gordon would set off pre-planted explosive charges to destroy the cave roof and expose Batman to the sun. However, Batman was aware of the plan all along, and in the ensuing skirmish, Gordon shot Batman in the back with a crossbow, and Croc threw him into a nearby chasm.
With Batman defeated, Two-Face immediately turned on Gordon and Alfred and attempted to kill them. Gordon was forced to use his crossbow bolts to kill Two-Face's thugs, using the last of his bolts on the last remaining member of the gang while leaving Two-Face himself still standing and armed with two loaded crossbows. Two-Face eventually cornered Gordon, gleefully stating that he would betray and kill Croc after Gordon was dead.