I spent over an hour in an endlessly looping battle with a boss on Final Fantasy IV.
I got to the water-elemental boss in Cecil's castle in Baron (that is disguised as the king). I'd whittle him down so far, and he'd go into a defensive mode, in a turtle shell where I'd do very little physical damage to him, and he'd heal himself while in that state.
Unfortunately, I already dumped all my magic into attacking him at this point, so all I could do was slowly whittle away his health and hope I got him before he healed again. And I was powerful enough that his 30-40 HP damage really wasn't affecting my characters much, so they weren't dying, either.
Didn't work, but I was so stubborn I kept at it for a damn hour.