It's either the merman(male) or the mermaid(female).
Mermaids or Mermen
A half cow, half fish creature is often referred to as a "mermaid" in folklore, though traditionally mermaids are depicted as half woman, half fish. There isn't a specific term for a creature that is literally half cow and half fish, as such a hybrid does not exist in mythology or biology. In creative contexts, it could simply be described as a "cowfish" or a "fisher" for fun, but these are not established terms.
Half human, half fish is a Mermaid.
The hippocamp (ἱπποκαμπος, from ιππος meaning hors and κάμπος meaning monster). They were the the half horse, half fish creatures that drove the sea-chariot of the god of the sea Poseidon (who was also the god of horses).
Ophitaurus is a mythical creature that is half fish half cow.
There is no fantasy creature that is half horse half human and NOT called a centaur.
I think you might be thinking of a hippocamp. http://en.wikipedia.org/wiki/Hippocamp
mermaids are creature(s) that live underwater... they are half-human and a half-fish.........
The close I got for half snake and half lion is a Griffin, which has a body of a lion a tail of a snake and a head and wings of a Eagle.
Mermaids are not real. A creature that is half human and half fish is biologically impossible.
Since the hippocamp is a half-horse half-fish creature, the tail is used for swimming.
The half horse, half eagle was a Hippogriff.