1st definition:
Piety =df what Euthyphro is doing, namely, prosecuting his father.
Fails because:
it does not show why other pious acts are pious (indeed, it does not show why Euthyphro's own act is pious).
2nd definition:
Piety =df what the gods love.
Fails because:
(a) Euthyphro holds that the gods differ about what they love and
(b) a single action cannot be both pious and not pious.
3rd definition:
Piety =df what all the gods love (Compare: the right, the good is what God loves or approves of.)
Fails because:
(a) the reason for applying a descriptive label is not the same as a motivating reason
(b) "what all the gods love" is a descriptive label applied correctly just in case it matches the facts, which in this case would be being loved by all the gods
(c) the motivating reason for all the gods loving some X is, Euthyphro asserts (pushed by Socrates), that X is pious (a descriptive label). But then:
(d) the motivating reason for the gods' love presupposes the truth of the descriptive label, to wit, that X is pious, and independently of being loved by all the gods (otherwise, there could be no motivating reason).