In normal speech, it's /jɪj'tso/ in IPA ([jиᵉjцó] in traditional Cyrillic transcription). In unstressed syllables, я usually becomes /(j)ɪ/ due to vowel reduction.
But if you pronounce it /jaj'tso/ ([jаjцó]), as written, this would also be OK: it will be understood as extra-careful pronounciation.
N.B. ц /ts/ is a single consonant that starts like t and ends like s.
So the woman's pronunciation which I hear in this thread is correct, but the new man's voice is not, as he pronounces an "a" at the end. If I understand correctly, the singular яйцо is pronounced with the stress on the second syllable, while the plural яйца should be stressed on the first syllable.