It's fair to say that for most of the story Don Juan Tenorio's heroic qualities are not much in evidence. A womanizing rake with a penchant for armed violence is not exactly someone we'd normally identify as a hero. If anything, he's more of an anti-hero in that though he's the central character of the story, he patently lacks the characteristics traditionally associated with the hero.
Nonetheless, this dashing young man does display heroic qualities as the hour of his untimely demise approaches. At long last, he finally repents of his many sins and ascends to heaven along with the spirit of Ines, the woman he so cruelly abandoned years before. On a charitable interpretation, Don Juan's actions are indeed heroic. He's recognized the immense damage he's done to so many other people's lives and is now willing to repent. Heaven is his reward.
If one were being less charitable, however, one could say that he only repents in order to avoid being dragged to hell. This interpretation paints Don Juan's actions in an altogether more self-serving, less heroic light.
In fact, it's much easier to make out the case of Don Juan as a villain. A violent murderer and serial philanderer, he certainly fits the bill of what a standard literary villain should look like. At the risk of indulging in armchair psychology, Don Juan displays all the hallmarks of a sociopath, a smooth-talking charmer who shamelessly uses other people to get what he wants irrespective of how much harm it causes.
Portraying Don Juan as both hero and villain makes him a more rounded character, much more readily identifiable. For all his many faults, Don Juan is recognizably human. It is because of this that we can identify with him to a considerable extent, even if we strongly disapprove of this many wicked actions. Don Juan, with his faults, is human in the very fullest sense of the word.