Nomura has recently stated that Dissidia: Final Fantasy is no ordinary action game, and in order to find out the story of this unique title Forever Fantasy decided to translate the trailer Square Enix has just recently released. Do note the random snippets make it tough to be 100% accurate.
Dissidia: Final Fantasy was announced in order to celebrate the Final Fantasy franchise 20th anniversary, and it is no surprise the story of the game will revolve around crystals, yet again. It seems as if the heroes that were chosen from each game (Squall, Zidane, etc.) are seeking out the crystals in order to learn the truth about the eternal battle between Chaos and Cosmos.
Note you've got to watch the trailer at YouTube in order for the video annotations to work.