I'm not sure why I'm giving you a serious answer, but I call bull shit on mermaids. :P
However, I can meet you... semi-half way on this because unicorns are another story. A horse-like animal with a single horn on its head. Horned four legged animals? (gazelles, deer, goats,) Common. Multiple breeds of horse like creatures in the world (donkeys, zebras,) check. Assuming one of those breeds, now extinct, once had a horn? Yeah. Really not that far-fetched.
Hell, I could buy that "dragons" existed at some point... as some lesser, surviving relatives of what we know as dinosaurs. (Fire-breathing or flying, probably not, but I could be wrong. It IS physically possible for an insect to produce a liquid roughly the temperature of boiling water with chemicals in it's abdomen, so it's safe to say that nature has some pretty weird shit out there already... maybe a lizard with a fire-starter cocktail in his gullet isn't all that crazy after all.)