It is a good idea to defeat the tentacles and then target the Octo-Leech. The Ice Shield and the Flame Mail can be equipped to absorb their elemental-based attacks. Ceodore can use Cura while the Hooded Man should use physical attacks. The Band ability Cross Slash can be used to kill the tentacles quickly.
In the PSP version released as part of Final Fantasy IV: The Complete Collection, the Octo-kraken and its tentacles switches their color scheme with the Cooler Mammoth and its tentacles — the purple Octokraken became red and the red Cooler Mammoth became purple. Both enemies are restored to their proper colors for the iOS release of the game.