In the OoT boss fight, you never interact with him while he's flying (aside from shooting arrows, which could really be left out without much loss to gameplay). So what you can do is this:
1) Have him fly up and off-screen.
2) Draw a shadow of it flying overhead. The shadow would move around the arena, chasing Link a bit as in OoT.
3) To have the fire-breathing portion, have a jet of flame come from off-screen in the upwards direction, hitting the ground overtop of the part of the shadow corresponding to its head.
4) Have rocks fall around the arena while this is going on.
5) The head shadow eventually finds its way to a hole, and Volvagia descends from overtop of the head shadow, entering the hole. As it enters, the corresponding parts of the body and shadow disappear as they reach the hole, the shadow moving steadily along the shadow path until nothing is left.
And then the rest proceeds as normal, with Volvagia popping out of another hole, etcetera.
Because its body is so snakelike, you could get away with just four shadow sprites - head, body, tail, and a corner-shaped body sprite for when it turns in mid-flight. And since shadows are just one colour, this wouldn't be very hard.