The baby

I hope the baby come into world healthy. This is fine because healthy is an adjective; healthily is an adverb. You want to describe the child, not the way the child is born - although if I were to use an adverb, I'd say, "I hope the baby comes into the world quickly."

More commonly I would say, "I hope the baby is born healthy."

If you have any questions, please let me know. :-)