Obtained the highest possible result in the battle to determine the fate of the world.
You need to finish the final bossfight against the 3 bahamuts with a 5 star rating. This is story-related and can only be done in Academia 500AF (Episode 6).
Take out the two smaller Bahamuts to your left and your right to make the big jet bahamut vulnerable to your attacks. It's highly recommended to use (almost) maxed out characters and a monster with at least 5000HP.
You can replay the bossfight at any time by using time reversal.