"Greek baptism"? I've seen dozens of Greek baptisms, as well as Russian ones, over several decades, and in every single case, the babies were completely immersed three times. Never seen "immerse the body of the bub and then pour water over his head". For one thing, in most, if not all cases, two people would be needed to do the honours: one to steady the child and prevent him from slipping under, and the other to pour water over his head.
The trick is to dunk quickly, wait a few seconds after the bub is lifted out to let it breathe, then dunk again, and so on. Do it properly, and there's nothing to worry about.