The pink reindeer is pretty tough. I usually try to run circles around the screen while avoiding the blue reindeer, sticking to the top and bottom of the screen. Definitely possible to avoid it though.
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Ohhh I didn't realize you can jump in the air forever lol. Maybe you could have included that in the in-game instructions, or used a different word (like "boost" or "flap"). Anyway gave the game another go and still didn't manage to beat it, the bit with the pink hearts and warping reindeers was just too brutal : D