I couldn't finish 'em. Looks like this's gonna get complicated.
1st battle Edit
The first battle against Cocytus is unwinnable due to story reasons. Either damaging her enough or receiving damage by a certain amount will cause her to use Glacial Dance to immediately end the battle.
2nd battle Edit
The second battle takes place inside Castle Avalon. Her physical-based attacks include Roundhouse, which inflicts Stun, and Slap, which inflicts Confuse. Blizzaga deals moderate Ice-Elemental Damage to either one target or the entire party. Glacial Dance, a multi-targets attack, inflicts significantly more damage than Blizzaga. Arctic Reverb, which also damage the whole party, does twice as much as Blizzaga and inflicts Sap. Benumb hits one target for a massive amount of damage and cause Stop. Shellshock places Magic Defense Down on everyone, thus making her attacks more lethal.
Firaga and Flare work great against this boss. A Magus double casting Flare or Meteor will inflict major damage. Fusion Abilities such as Gigaflare, Phantom Rush and Midareyuki are also godsend. Watchout for Magic Defense Down, which can be negated by casting Shell, as it is a pain when combined with Cocytus's Ice-based attacks.