Most of its attacks are nothing new to you. There is a basic attack, Hit (50% more powerful), Firaga, Blizzaga, Thundaga, Quake, Tsunami, Northern Cross, Southern Cross, Flare Star, Meteor, and Ultima.
Lucky (or unlucky?) you, Ultima is not some random attack Ultima Buster can use a whim like Brachiosaur. Rather, it is only used every twelve times you hurt him. Two turns later, he’ll attack you with Ultima, easily able to deal 2,500 damage. Unless Celes/Gogo uses Runic.
Strategies? The good one you should be able to access by now is a very lazy but effective one. Put Reflect on everyone and, for the most part, Ultima Buster will destroy himself with Reflected attacks. Granted, you will need to heal somehow from Meteor, etc., but eventually Ultima will come up. To survive it, you’ll need Reraise on yourself prior to that, have someone use Runic, or use Quetzalli at the second yellow flash.
And if you don’t like being lazy, or just can’t heal like this? Have someone dedicated to casting Reraise on your party, then Hastega and hopefully Mighty Guard. Put Reflect on the party members most prone to magical damage, then simply use combos of Quick and Ultima/Meteor/Flare, or something. You know, high damage stuff. You should know what works. Be sure to replace Reraise after Ultima, though!
After Ultima Buster falls, you’ll be able to use a Save Point. Granted, a Save Point on a bloody battlefield is not my first choice of sleeping places, but, hey, you take what you can get. Use a Tent, Save, and let’s go.
Go south and out of the door. After that nice falls, go upstairs into another room, which happens to have a bunch of pipes. Ah, just like Mario. But more violent? Anywho, go into the leftmost one.
Back outside (not necessarily a good thing), go southwest to find a Force Shield . Go south and through the door. Here, open the chest for a Ribbon and step on the switch nearby. This will let the first party advance, but let’s wait a bit. Go back outside and go west to find some Force Armor . Go east and through the doorway. Inside, go north to find a red-carpeted area. Heal up and head over to the dragon.