This is pretty easy. Head to the Opera House, found on the southwest portion of the southwestern continent; south of Jidoor and west of Maranda. Some good ideas before the fight include Float pre-fight and Gaia Gear. Having some Water/Wind-based is good, too. And, of course, save before entering the building.
Once inside, speak with the Impresario and he’ll speak of the dragon. As you head northeast to the switch room, notice how that the orchestra is playing despite a dragon being mere feet from them. It’s odd; maybe the Impresario was in the middle of some odd satanic sacrificial ritual before we arrived?
Continue into the switch room, questions unanswered (and upside-down pentagrams unfound), and trigger the second switch from the right to start a fight with the dragon itself.
The Dirt Dragon – erm, EARTH Dragon can use a basic attack, Honed Tusk (which is about five times as powerful), Quake, Landslide, Magnitude 8, and 50 Gs (which will cancel Float). Honed Tusk will often appear as a counterattack.
Begin the fight with the usual – Kirin, Fenrir, and Hastega will settle defense. Bismarck and Leviathan are good fill-in Espers for offense. Your offense probably can’t consist of Wind/Aero or Water spells unless you bring along Strago, which I myself didn’t. Flood is a possible spell, though probably not taught yet. Then again, it all depends.
Not like it matters all that much. Casting Sleep and Slow on the beast will circumvent damage for a fair while. Beyond that, spells are the best for this, to prevent reawakening. Pretty much any will work – Ultima, Flare, and Flood are my preferences; if you have Strago, think of Aero; Shadow, Water Scrolls; Mog, Water Rondo or Wind Rhapsody.
Yep, that’s it.