Most people seem to want to use Batman: Arkham as a template, but obviously, not all superheroes are Batman, so they probably wouldn't work in a stealth game. What genre would be most appropriate for each hero? If it would be easier, you can suggest a video game that you'd like to influence it.

Green Lantern-The World Ends with You or The Wonderful 101
Considering how the main focuses of the Green Lantern Corps is that they're space cops who can create anything with their rings, games that focus on drawing mechanics would work well with them.

Wonder Woman-God of War
Let's be real. Everyone has thought of this. While WW's more routed in Greco-Roman mythology, I think the 2018 gameplay mechanics would be more fitting as they allow for more customization.

Aquaman-Nier
I watched the movie and instantly thought "This would make a great Action RPG". The problem is that there aren't many RPGs with good water mechanics, so that would be a hurdle. Nier and its sequel would probably be the closest RPG to what i would be thinking of.

Superman-Final Fantasy VII REMAKE
This is easily the trickiest because of how picky most people are with what they want in a Superman game. Even worse FFVII hasn't even come out yet, so I'm basing everything off of trailers and what I think the game would be like. The only thing I'm sure of is that the enemies are actually able to hurt Superman. There are many things capable of hurting Superman and they really aren't rare either. The idea that Superman shouldn't have a healthbar feels ludicrous to me.

Flash-Sonic
Does this even need to be said? The problem is mostly like Superman's problem of creating convincing threats and enemies. If we can make the mechanics work, then why not?