Really interesting mechanics.
I had the most luck with the chicken, and even managed to get the egg, but the dragon slew me before I could get to the bottom.
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The dragon is tricky and will never stop following if you have her Egg because she's a good mother ;) A tip I can give is don't get in front of her. If you escape with the Egg and replay with the dragon mount you will see why =D
Thanks for giving it a shot! I and am still playing through With Hooves of Fire it' lots of fun!