Yeah, normal names first, and I agree the story made The Dark Knight work so well. Many of the other nicknames lack that punch, but Dark and Knight come with so many connotations each.
The Amazon Princess is so on the nose, but if the second film deals more with Themyscira and a political subtext, it could work. Come to think of it, leading with 'the Amazon Princess' does work to break the link with any pre-conceptions of Wonder Woman. Could be smart, depending on how much you're updating her. King of Atlantis could be similar for Aquaman. The Amazing Amazon doesn't really say anything about story at all, does it?
The Fastest Man Alive is equally light on poetry, but if the story is against the clock, it could mean a lot for that story. Scarlet Speedster is another generic descriptor, same with Emerald Archer, Emerald Knight and others. No poetry, no real meaning, just nicknames.
Batman has more to share, but Caped Crusader has a little cheese on it still from the 60s, and while Shadow of the Bat sounds nice, especially for a Robin-centric story, then we're not talking about
Speaking of... it'd be quite interesting to see "Boy Wonder" as a film.
My thoughts now:
Man of Steel, Last Son of Krypton, Man of Tomorrow
The Amazing Amazon, The Amazon Princess, The Gods' Favorite Daughter
The Flash, Flash 2, The Flash 3
Green Lanterns, The Green Lantern Corps
The King of Atlantis, The King of Atlantis Returns, The King of Atlantis Triumphant
Martian Manhunter
Cyborg
Arrow