It should be /ˌhɑɪpoʊˈkaɪmənɒn/ “high-poe-KIME-uh-non".
The pronunciation of the consonants is unproblematic.
The stress is clearly on the third-to-last syllable, as all the relevant languages involved agree on this (Greek, Latin and English). The prefix “hypo-” already has an established pronunciation in English, which I would advise using (/ˌhaɪpoʊ/, or “HIGH-poe”).
The pronunciation of the last syllable is a bit harder to determine, as the Ancient Greek neuter suffix -on is usually converted to the equivalent Latinate suffix -um in English words. (For example: bacterium, etc.) However, a good analogy for the vowel sound can be found in the word “automaton.” Some people pronounce it as /ən/ “un, while others pronounce it as ”/ɒn/ “on.”
The second-to-last syllable is unstressed, so will likely simply have a schwa sound in it, /ə/, “uh” or “ih.”
What remains to be determined is the pronunciation of the vowel in the stressed syllable. In general, the digraph “ei” in Greek-derived words represents a “long i” sound, and it is sometimes even interchangeable in the spelling with an “i.” Traditionally, English speakers have pronounced this as the English “long i” sound, /aɪ/, as in the words “Deimos,” “meiosis,” “eidolon,” or “irony” (from Greek εἰρωνεία eironeia). Some people might try to use a pronunciation closer to the Modern Greek, and instead use /iː/ (an “ee” sound), but this is not a common pronunciation for this spelling pattern.
Although the spelling of the stressed vowel suggests an /eɪ/ “ay” sound to the naive eye, this would be an irregular pronunciation, not in accordance with either the traditional English pronunciation or the modern Greek pronunciation. I would therefore recommend against it.
So: the overall pronunciation would be /ˌhɑɪpoʊˈkaɪmənɒn/ “high-poe-KIME-uh-non”, or if you wish, /ˌhɑɪpoʊˈkiːmənɒn/ “high-poe-KEEM-uh-non.”