This is a Totema boss battle. You enter the Nargai Cave and Marche sees a ghost, but doesn't feel scared. He follows the ghost farther into the cave. Then Marche is warped to another temple-like place. Marche follows the ghost and reaches the floating crystal. Then the Totema, Adrammelech, comes out with some dragons. The dragons are pretty much like other dragons you've fought, with Breath powers. Adrammelech knows the Firestream attack, allowing him to attack several of your party at once if they're all on the same line. This is a powerful attack. Try to keep your clan members from being in line with each other. If you have moogle or nu mou clan members, they can use their JP to summon their Totemas. It will certainly help. Be sure to focus your attacks on Adrammelech, because the battle is over once he is defeated.
When it is over, the crystal shatters. Babus comes up to Marche in the cave. After an appearance from Mewt, Babus asks why in the world you're trying to take away Mewt's world, asking what could possibly be so great about the other world that Marche would want to return to it at the price of destroying Mewt's world. Without waiting for an answer, Babus leaves.
With Adrammelech defeated, Bangaa get his Totema, which hurts all enemies on screen for a large amount of HP.