Barbariccia sometimes counters physical attacks with the powerful Lightning spell, which does upwards of 500 damage to the party, and otherwise uses strong physicals (which are Wind-elemental and have a 20% chance to inflict Silence on the target) and Tornado, which reduces HP to single digits. Rosa and Cecil should cast Shell and Protect on the party while Kain jumps and Yang builds up power with Focus. Once Kain lands and Barbariccia's wind shield falls, the party should attack her and use Rosa to heal.
During the battle in the Giant of Babil, Barbariccia is permanently locked in tornado form because Kain is not in the party, and thus is immune to all physical attacks, but in this battle she has a weakness to the Holy element.
Barbariccia is a demon in the Inferno of Dante's Divine Comedy. He is one of the 13 Malebranche ("Evil Claws") who guard Bolgia Five of the eighth circle of Hell, Malebolge. Vulgar and quarrelsome, their duty is to force the corrupt politicians to stay under the surface of a boiling lake of pitch.
His name means "Curly Beard."