Always found Draygon easy before I managed to get the electrocution method down pat.
First, destroy the turrets while the Evir are leaving. There's a piece of foreground on the floor that looks something like a
Sciser right in the middle of the room. Crouch here holding aim diagonally up with Super Missiles selected and then follow this method:
1) If Draygon swoops in quickly from the side, fire a Super Missile and quickly Morph Ball down to avoid being clipped by the tail, rolling if it looks like you're going to get hit. Always roll
towards Draygon (ie: in the direction it came from, not the direction it's heading.).
2) If Draygon glides in from the side slowly, spewing globs; just spam missiles as fast as you can for as long as you can before running off to the side Draygon is heading too, hopping onto the raised floor, and jumping over Draygon. Flash gits such as myself will do so with a wall jump.
3) Draygon always enters the room from the same side it leaves, unless it catches you; in which case it'll just come from the same side as last time.
At least that's how I remember it. It's been a long time since I learned the perfect electrocution method, and unless you're doing a low Energy Tank run it's perhaps the best method to kill Draygon. Health shouldn't matter, there's a recharge room above Draygon's, so you've no excuse to fry the bastard.