Well, I'm giving you a bonus since Leviathan is right after Bahamut.
Bahamut:Bahamut is a pushover, honestly, though he has one major attack, Megaflare, that can decimate a weakened party. What does this mean Well, at the very least, it means you're going to want to keep your party fully healed for the duration of the party. Have your party's healer cast a party-wide healing spell (Curaga, Curaja) each round to ensure this. Bahamut will strike twice per round, otherwise, chipping away at your HP until he breaks out the big guns, so the battle can deceive in this way. Even though the dungeon leading to him is simple enough, why play through it again if you don't have to Stay alive by healing and delivering Bahamut a devastating onslaught of physical attacks, spells like Bio, and anything else you can throw his way.
Leviathan: Leviathan is fairly easy to defeat (just like Bahamut was), but he does have a duo of strong attacks that can frustrate your efforts to defeat him as easily as you would probably like to. One attack, Blizzaga, will attack a single target and devastate that member of the party (with a high potential to kill him or her). The other attack, Tsunami, is a party-wide attack that has like potential to the aforementioned attack. Healing is a necessity here, but you should be able to deal him enough damage with high caliber physical attacks and lightning-based magic, like Thundaga, that in three or four rounds, he will be no more. He'll give up his summon, the Leviath Summon, as a result.