If we want to get technical, Wikipedia (I know) defines a hero as:
A hero (heroine in its feminine form) is a real person or a main fictional character who, in the face of danger, combats adversity through feats of ingenuity, courage, or strength...The original hero type of classical epics did such things for the sake of glory and honor. Post-classical and modern heroes, on the other hand, perform great deeds or selfless acts for the common good instead of the classical goal of wealth, pride, and fame.
That fits, if you consider the violent oppression of a police state to be in the common good, which Dredd most sincerely does. He's certainly not a tragic hero in the Aristotelian or Shakespearean sense (a great man doomed to a tragic end by a fatal flaw), nor is he an anti-hero (who may do good but for selfish or evil motives). Wiki did suggest the intriguing "anti-villain" or sympathetic villain:
The sympathetic villain or anti-villain is one with the typical traits of a villainous character but differs in their motivations. Their intentions to cause chaos or commit evil actions is driven by an ambiguous motivation or is not driven by an intent to cause evil. Their intentions may coincide with the ideals of a greater good, or even a desire to make the world a better place, but their actions are inherently evil in nature. An anti-villain is the opposite of an anti-hero. While the anti-hero often fights on the side of good, but with questionable or selfish motives, the anti-villain plays a villain's game, but for a noble cause in a way that the audience or other characters can sympathize with. They may be more noble or heroic than an anti-hero, but the means to achieve their ends are often considered exploitative, immoral, unjust, or simply evil.
(Sadly, none of the suggested examples are much like Dredd - Daenerys Targaryen, Eren Yeager, Itachi Uchiha, Killmonger, Lelouch Vi Britannia, Magneto, Doctor Octopus, Sandman, Severus Snape, Thanos. (Again, I know), but they are all anti-villains contrasted against heroes, Dredd's the protagonist, an anti-villain against worse villains)
IMO, he is a hero within the parameters he was bred and programmed for. He is the ideal of how the Judge system was supposed to turn out but sadly 99% of the force are merely human, which is why MC1 isn't an oasis of peace and happiness. If every judge was as dutiful and dedicated as Dredd, maybe it would be, or maybe the entire philosophy is flawed as it misunderstands human nature.
So hell, I don't know. I do know that if some creep was holding a laz-knife to my throat, I'd rather see Dredd riding up than my elected representative.