While Barbariccia is in tornado form, she counters all weapon attacks (with the exception of Kain's Jump which forces her out of this form), with strong physical attacks and the Maelstrom spell. 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.
When she returns to her regular form, the player should start using Cecil's and Cid's attacks, Yang should use Focus, and Rosa should buff the party. For the battle in the Giant of Babil it would be best to have Rosa (if she has learned it) or Fusoya cast Holy, and RydiaSummonMist Dragon to take her down quickly.
Barbariccia sometimes counters physical attacks with the powerful Lightning spell, which does upwards of 500 damage to the party, and otherwise uses strong physicals 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.