Mythical heroes are unlike everyday hero which requires mere bravery or something slightly extraordinary. A mythical hero requires a greater feat beyond extraordinary, they require power to achieve their heroic feats, such as Hercules requiring massive strength to defeat Hydra, or Perseus with his demigod talent, killing medusa.
For these heroes to be mythical heroes, they have to be related to the respective mythical gods, like how Hercules being demi-god, having Zeus as his father. The world they live in also requires mythical beast which only a true hero could slay. However, when two great power clashes, it also creates myth. Such examples can be seen through the epic fight between Achilles and Hector in the Trojan War. However, Ajax, Oddyseus, and Phoenix who also went within the same war did not gain the same fame as Achilles, this is clearly shows how an epic clash could led a hero to be a mythical hero.
These are myths circling around the mythical heroes in the past. However, due to the past mindset of female being inferior to male, except for egypt, there isn't a single mythical heroine in greek history. Heroine only appears after 1990s, which however, still portrayed as evil in most of the case. The only strong support towards female heroine is actually Japan "manga and anime" which has a huge percentage of around 50% to 60% having heroines instead of heroes.
Hero can be constructed, or rather grouped to different archetype. In most cases, especially the past, main hero is always a warrior, a person of the light, doing justice, banishing evil. This archetype groupings expanded the range of main character/hero attitude. Now, heroes vary their archetypes, being either a wanderer who prefers travelling alone, or being extremely naive as an innocent, or an orphan who is realistic and usually selfish, or a magician who is innovative and charismatic, however weird or unique.
Even mindsets of hero varies widely, the reason behind their persistence and keep moving forward, is no longer solely based on the light. There are heroes driven by hatred and revenge, or heroes who has ulterior motive all along. Some heroes even go against God and the world in order to achieve their dream, even when they know that what they are doing has much lower chance of success than mere sacrifice.

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