HERE'S THE KEY TO THE SNAKE! The snake actually follows a very predictable pattern. It will pass on the top of the fight area with its mouth open (attack), then with mouth closed (harmless). Then it goes towards the bottom, and does the same thing. It alternates between mouth open and mouth closed, and every other pass it switches its path. The trick is to gather fairy flies while it's passing with mouth open above or below you, and then switch to the other area (top or bottom) while its mouth is closed. Once I figured this out, it only took a minute or two to win the fight.
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