Yeah you gotta beat it with every character to unlock "True Story Mode", as each character's first ending is a 'key' that Aeon uses to meld the timelines back.
However, to truly mend the timelines the strongest character needs to defeat the final boss.
This means that to see the true endings and what happened to every character, you have to beat the game with each of them. This includes Aeon, who is unlocked after the first endings are done for the other characters, from what I recall.
I haven't unlocked everything in Castle Mode but you don't really get anything with that mode aside from the unlockable trinkets, I believe.