Anthony "Tough Tony" Bressi was a mid-level mob boss in Gotham City. Batman tolerated him as 'small fry', occasionally opposing his shady operations but otherwise using him for information on the status of Gotham's underworld.
Hailing from a major crime family, Tony Bressi surfaced in the fifth year of Batman's career. He had recently inherited the Gorfinkel Export and Import business, which made him a very wealthy man. Using the business as a front for illegal activities, Bressi managed a protection racket that netted him thousands of dollars in filthy cash. Using the money, Bressi married and bought a huge mansion for himself in the Somerset district of Gotham City.
Spreading his influence across Gotham, he soon was up to his elbows in every shady deal involving the local mafia. His position brought him to the attention of Killer Moth, who offered his services as a mercenary supervillain, willing to defend criminals from the likes of Batman and Robin. He pointed out that Bressi had bribed much of the GCPD to look the other way in his affairs, but that he would be unable to do the same with the Dark Knight. Bressi found Killer Moth laughable and refused his offer. In the wake of their meeting, he had his henchmen destroy the Moth-Lantern, Killer Moth's attempt at a Bat-Signal, which was broken before he could even use it.
Plotting revenge, Moth later returned to fight against Bressi in Batgirl: Year One. By this point, Bressi had purchased a nightclub known as the 'Stripping Post', where he spent most of his evenings. Killer Moth returned and demanded a cut, and, when Bressi again tried to have him thrown out, Moth had fellow costumed criminal Firefly torch the club. Bressi's hand was burned during the incident, but he otherwise escaped unharmed. Tony then hired two of his thugs to impersonate Killer Moth and Firefly, framing them for a crime as retaliation. Instead, the real Moth and Firefly tracked the doppelgangers to Bressi's mansion, where they were trying to hold Police Commissioner James Gordon hostage. To complicate matters, Black Canary and Batgirl arrived on the scene. Firefly proceeded to burn the mansion down in the ensuing battle, much to Bressi's horror. He and his wife escaped the blaze intact, however, Tony even helping Batgirl drag Commissioner Gordon to safety.
His revenge against Bressi exacted, Killer Moth never dealt with him again. Five years later, an older Anthony Bressi had maintained control of the unions in Gotham City, otherwise working quietly at his export business. His protection racket and other schemes continued to be complicated, however, by costumed heroes such as Robin and the Huntress.
Eventually, his hopes for successful operations without the interference of heroes were raised when Batman's back was broken by Bane. Jean Paul-Valley succeeded him temporarily as Batman, and when he learned that Bane was attempting to strong-arm Bressi into turning over the unions to him, he raided one of Tony's establishments. Jean-Paul gave him a savage beating, leaving Bressi with a permanent scar on his cheek. Bressi explained his two children had been kidnapped by Bane to force him to cede the unions over. Valley then arranged for a sting operation. He would wait at the Gorfinkel warehouse in the Salerno district, where the deal was going down, and Bane handed over Tony's son and daughter. He would then capture Bane, or his henchmen who were present at the exchange. If Bressi tried to get out of it, the new Batman threatened to make him eat his eyes.
As the deal went down, Valley attacked before Bressi's children could get to safety, endangering them and infuriating Robin. Tony reached his son and daughter in time, protecting them before they could get hit by stray bullets. The GCPD promptly raided the warehouse, capturing Bane's men, all of whom had been beaten so savagely by Jean-Paul they were in no shape to talk about Bane's whereabouts. (Batman #499)
During the events of Batman: No Man's Land, it has been implied that Tony Bressi abandoned Gotham to its fate and left the city with his family. It is possible he relocated elsewhere to live out a quiet life, or simply moved his criminal operations with him. Either way, the new generation of mafia which moved into Gotham following the great disaster appear to have taken over Bressi's former services and turf.