ὑπο (usually transliterated “hypo”) is an adverb that can mean “under”, “at”, “by”.

ὁ ἵππος (usually transliterated “hó híppos” or only “hippo”) is a noun for “horse”. Greeks already use this noun to form other words, using the steam “ιππο-”, like ἱππο-πόταμος (hippo-pótamos, “river horse”), ἱππό-κομος (“horse-hairy, with a horse hair”) and many others.

It might be worthy to notice that there’s no “h” in Greek. This consonant appears only when we transliterate greek words that has a “rough breathing” stress on a beginning vowel; so we use “h” to mark its “strong/rough breathing” pronunciation, quite like the “h” sound in english “hot”, for example.

I had always thought be a hypocrite was to criticise others for something that you do yourself. As such, I had supposed the etymology to be something like “under critical”; that is, you were not critical enough of your self.