Mizuchi has three abilities available to it. Its Bite is a standard powerful single-target physical attack, Freezing Eye renders the party Water-weak, and Icy Breath inflicts heavy Water damage on the entire party and can inflict stop.
A team of two Templars and two Black Mages can devastate Mizuchi. Templars should make use of Rampart as needed to keep the status on everyone, and Black Mages should use Thundaga to exploit Mizuchi's Thunder weakness. All party members should have the Red Mage's BP Recovery support ability equipped to gain 2 BP whenever Mizuchi uses its Freezing Eye ability. It's also advisable to have the Time Mage's Stop Immunity support ability equipped as well, otherwise Mizuchi's Icy Breath attack can freeze your characters for multiple turns.