Final Fantasy IV
Final Fantasy IV really did have awesome, awesome battle music.
This is FFIV's offering in the Major Boss category. And somehow, it manages to be even better than it's all-time-great Minor Boss music. It starts with one of the great opening riffs--that's another list I'll compile sometime, my favorite opening riffs, and this one will rate highly--and remains intense, high-tempo, and aggressive throughout, just like your battles with these Elemental Bastards.
I have no idea what they're really supposed to be called. In the original SNES "Final Fantasy II" they were called the Four Fiends of the Elements, which I read for about a year as the Four Friends of the Elements before I took a level in Hukd Onn Fonix and figured it out. Whichever mp3 I put on my player years ago is called "Battle With Golbeza's Four Emperors," and I've seen them called Lords a few times.
Well, they were all bastards. So the Four Bastards of the Elements suits me fine. Well, except Cagnazzo or however the hell you spell the water guy's name. That guy got his ass handed to him deep-fried courtesy of Tellah's Bolt3. But Rubicante more than made up for it by being, in many ways, a truly magnificent bastard. All in all, they were one of my favorite Quirky Miniboss Squads. (Though, as long as we're invoking tvtropes, Rubicante was really more The Dragon to Golbez, who turned out to be The Dragon to Zemus, and... yeah.) And they have the heart-pounding battle music to back it up.