The only heroes I think deserve their title are those who make no claim to being heroes. You know, Jon Snow, not Daenerys Targaryen. The former doesn't make claim to his own greatness, whereas the latter has half a million titles for what ultimately came down to the most unwilled thing of all, her birth.
The hero that marinates in his own greatness takes credit for something that isn't his own. He ignores the genetic and phenotypic (intelligence, muscles, etc.), familial, upbringing, social economic status, and other variables that make him who he is. Yes, the best hero is the one who asserts his will the most, who takes the most risks. But who can really measure that given the complicated inner world of any particular person? What I see as an amazing act of will might really be an act with the highest motivation and a hidden payoff. The younger Arnold Schwarzenegger is indubitably a hero of bodybuilding, but he's also the guy who said that working out is like reaching an [bless and do not curse][bless and do not curse][bless and do not curse][bless and do not curse][bless and do not curse][bless and do not curse]. Why should he be a hero compared to the average Joe who puts in eight hours a day and gets no praise?
But there are definitely heroic acts. A man who risks death to save an anonymous child is unambiguously heroic, even if the man himself isn't a hero in the fuller characterological sense. Yet how many people consistently commit heroic acts like this, where the hero genuinely makes a risk over and over again? These types of heroes are short-lived for obvious reasons.
The hero is a flower lavished with praise without considering the garden and soil that made him possible. He as the individual may indeed put in the sweaty will-based work without which he wouldn't achieve the status he has, but this is only the tip of an iceberg, the rest of which is a collection of givens, and no outside person can truly know how hard the hero has worked to attain his status given these givens, centering on motivation, which always pushes a person and so makes willing easier.
The best hero is the one who gives away his status as hero. The hero of humility who reflects back his heroness to the family and upbringing and ultimately the very universe that placed him where he did at the time it did. He realizes like the poet Pablo Neruda that life is a borrowing of bones. You didn't create the prerequisites to becoming who you became. A hero is just someone with a lucky set of prerequisites and not even necessarily a strong will, or any will at all, to actualize them into his heroism.