Link from The Legend of Zelda has a problem similar to one Batman famously faces. In a manga story within the Hyrule Historia, a Skyward Sword era Link finds that Hyrule is like Gotham. It may not be as modern or gritty, but the citizens share a commonality.
The Hyrule Historia is a collector's volume from Dark Horse Comics that was published in 2011. It features artwork from the numerous entries in the video game series and establishes the chronology of the world. However, it also has an exclusive short manga story celebrating the game's 25th anniversary from the team that wrote other The Legend of Zelda manga. This manga is focused on the very first Link, who was established by the story in The Legend of Zelda: Skyward Sword.
Akira Himekawa - the unit name of A. Honda and S. Nagano - tells of how the land of Hylia was saved by the very first Link. At the start of the story, he is locked up in prison. Other Hylians enter his cell where he is shackled, coming to seek his help. He was wrongfully imprisoned, but the person who framed him is dead, meaning he can be released now that his fellow Hylians need him. Having been treated as a hated figure, Link is still expected to risk his life to save the kingdom once it's in trouble - a problem Batman is very familiar with.
In Batman Begins, Detective Gordon says the titular hero is the "hero Gotham deserves, but not the one it needs right now." For years, Batman is vilified by the citizens of Gotham. He routinely saves the day, and is even expected to be around when things go wrong, but that doesn't make him the hero that the city wants or applauds. Batman is a hero who is always willing to stand up and protect Gotham, even when the city turns its back on him. In this manga, Link is facing a very similar dilemma within Hylia.
Link is the legendary hero of Hyrule, fighting Ganon/Ganondorf through different reincarnations and eras. This is the first Link, from who all the others descend. His crime is not revealed - and it doesn't have to be. What matters is that he is a hero who not only wants to protect Hylia, but is directly called upon to do so despite having been mistreated by those who now need protection. The very same people who want his protection are the ones who imprisoned him and said they didn't have a need "for a powerful hero." They only care about what he can do when it is on their terms and when they are in danger. Nonetheless, Link is willing to defend his home in the same way that Batman is willing to defend Gotham - no matter what others think of them. Both heroes even espouse a relationship with their lands separate to their people, with the Dark Knight considering Gotham his city, and Link assuring Hylia that he will always defend it, regardless of its people's actions.
The Demon King is coming, bringing the potential ruin of Hylia, and that is all that matters to Link. He is a hero, and as fickle as Hylians may be, the issue at hand is bigger than revenge or a lack of appreciation. It is a matter of life and death, which he takes very seriously. Typically, Link's adventures in games set later in The Legend of Zelda's chronology frame him as a legendary hero that people are grateful for, even if he seems like a myth. However, that legacy is one that was hard-earned by the first Link, as he suffered not only at the hands of his enemies, but also the hands of his fellow Hylians. Hylia can be about as grateful to The Legend of Zelda's Link as Gotham is to Batman, but both heroes will nevertheless give their all when evil rears its head.