I was skimming through the GameFAQs forums and while on the SO4 board, I found these cool looking battle videos from the game and posted them here for the fans viewing plessures.
http://www.gamefaqs.com/boards/genmessage.php?board=946860&topic=47903841
http://dl.square-enix.co.jp/so4/7sgam2cpx.flv
http://dl.square-enix.co.jp/so4/ki746g2qa.flv
http://dl.square-enix.co.jp/so4/qol66dwk8.flv