Full strategy guide for this achievement.
If you watch the video closely you will notice how I move with the dragons,DO NOT GO HEAD ON UNLESS YOU WANT A FIRE BALL TO THE FACE!
Make sure your slowly swerving around to the side of the tunnel exit there about to come out of, and again don't let them face you. Same goes for the pipes leading underground, don't bother going under just head to the other side and don't loose track of whatever one you choose to go for first, always spam the or button before they exit the pipes you'll get a good few hits in.
They will sometimes go into a spinning motion, simply move
with them as they do this, THIS IS WHERE MOST OF THE DAMAGE WILL BE DELT
Good luck and remember it's a guide showing the strategy rather than the full fight, just be extra careful and go for 1 at a time, I found gong for the red dragon first was a lot easier.
Hope this helps if your struggling!