The problem with the hero archetype is that it is so easy to be dull. The hero starts out as a pauper, a trainee assassin or mage, a farmer, and then goes on a mighty adventure where a darkness must be stopped. That is, in its most simplest form, the hero narrative.
Take inspiration from boring stuff. This may sound counterproductive, but as dull as the classical hero is, there is a reason every hero’s story is based on it. The Matrix, Star Wars, and The Hobbit are all famous examples of the hero’s journey done brilliantly. There must be something there that you can use.
For example, the idea of your hero not being well off in the beginning and then working their way to the top is a storyline that will make the readers empathise with your character. They will be happy when the hero prevails and sad when they fail. This is the simplest tool for creating empathy for your hero.
Give them flaws. I don’t mean that their hair stands on end no matter what is done to it (I’m looking at you, Harry Potter). Dalinar in Brandon Sanderson’s The Stormlight Archive is a brilliant example of the hero character being reformed in the fantasy genre. He’s done some bad stuff (no spoilers for anyone who hasn’t read it yet), really bad stuff, and that part of his character is still there a little. He’s still brutal and has to think about what the right things to do it. That is the kind of hero you want to read; one who struggles with what the right thing is. (There is of course a lot more to Dalinar but I won’t get into that here).
Kvothe in Patrick Rothfuss’ The Kingkiller Chronicle is brilliant at everything he puts his mind to, however he’s terrible with money, has a strange obsession with women, and is overly prideful. These flaws might not sound like much if you haven’t read it, but for his character they are detrimental to his journey. That is what is needed – a flaw, or flaws, that effect the life of the hero.
Make them weaker than the villain. By this I mean don’t make your hero overly powerful. If we know that the hero is invincible, we know how their story will end from the beginning. The readers needs ambiguity on that matter.
If you write a hero as powerful as Superman or as clever as Doctor Who, we know that they will win. I know that both examples have merit, but we certainly don’t need more of the same!
Make your hero struggle, really struggle, to get to the point where they just might be able to defeat the villain. A great example of this would be CW’s The Flash. Barry Allen has to increase his skill a huge amount to be able to defeat the main villain (I’m talking about the first couple of seasons mostly). We really see him struggle to fight doubt and pain – this makes for an exciting story and we really care about the hero because we see how hard they are pushing themselves.