The Octomammoth was once an ordinary octopus that was mutated by unspecified "underwater experiments." Tellah comments that it is "an octomammoth," indicating it is not the only mutation of its type. Though no others appear in the game or its sequel, Final Fantasy IV: The After Years, two similar monsters appear, Octo-Kraken and Cooler Mammoth. Palom mentions that the Cooler Mammoth once gave Tellah trouble, indicating it may be the same creature.
The Octomammoth can be rough if the player has not been battling along the way. Cecil should have collected the Shadowblade and some Hades-type armor and use Darkness, then use physical attacks with Darkness status. Tellah and Rydia should use Thunder, and occasionally, if they have enough MP, summonChocobo with Rydia. The party should heal with Cure or, hopefully, Cura when Cecil and the others get weak. After losing a percentage of HP, the beast's tentacles will vanish, and when it has about four left, Tellah will warn that a wounded beast is dangerous. Afterward the Octomammoth will slow down, but deliver massive hits that could possibly defeat Tellah or Rydia in one hit, and leave Cecil weak.
This battle also follows the patterns of its source, but it is likely the player will not be able to hit both targets unless the Black Mage has incurred enough damage to build his Soul Gauge sufficiently. The player only needs to cast each spell once, though, and can continue to hack at the beast until it falls. Since it initially has all eight arms, the Octomammoth strikes fast at first, but not hard; it will slow as its limbs drop away, but hit harder. White Mages can again Protect and Cure allies to soften the blows dealt.
In Elite mode, the Dark spell and high-level Thunder magic should make short work of it, with White Mages assisting as above. Tellah waited behind a Bonus Quest for the player, prior to The Burning Blade.