What happens if you die trying to beat the Thunder Dragon's Challenge?
Solution 1:
You get a game over.
This doesn't mean much in terms of actual gameplay since you can continue as normal, but you will have to start the challenge back from the beginning, after reloading from your last save.
Solution 2:
Game Over. You can then continue from your last save point. Fortunately, there's a bird statue a short distance from the Thunder Dragon.