Defeated a powerful enemy with valiant skill.
This is story-related and can only be done in Episode 4: Augusta Tower (AF200).
The bossfight against Demi-Fal'Cie Adam is not missable. You will have to beat him two rounds in a row, both with a 5 star rating.
Set the difficulty down to easy in your game settings. This is very helpful when you want to get it in your first attempt. Start out with 3 ravagers, kill the 2 manipulators and stagger him. You will have plenty of time, so there is no need to worry when playing on easy.
Round 1 goal time = 3:37
Round 2 goal time = 5:58
Make sure none of your team members is going down and beat the cinematic event perfectly.
You can replay all levels and fight the bosses again. Don't worry if you missed this one your first try, you can still get it without starting a new game.