Each individual flame only needs to be put out once. Since you can move the crate as you are dying, this means on most levels you only need 1 death or less just by jumping in the fire and scooting along until you put out the whole pit and die. Then the level would reset, but you don't need to put out those flames anymore. It only adds a small amount of time but for some levels, it's slightly more challenging.
Death would be required for many of the levels. I believe you need to die 7 times in order to win.
What about sections? The game is clearly designed around 5 different sections based on the chest colors. YOu could do 1-5, 6-10, and 11-15.
I've been thinking about this, what if we had a category for putting out all the fires and winning? It's only slightly longer but more difficult