You must watch all story cutscenes in Classic Arrange mode. There's two ways to do this:
Legitimate: Play through with every character in Arrange mode to unlock their story cutscene. Will take around 3-4 hours.
Cheat code: Hold
+
+
+
on the "Story Replay" under options. This will unlock all story cutscenes you can watch. Simply watch them all to unlock the trophy (I think you may only have to watch the bonus one but I can't confirm as I watched them all).