i would think, second to actually removing parts (or all?) of the shell, the next hardest thing would be maintaining sterility...
well, actually sterility WHILE removing the shell, and then after... i've seen where they grew chicks totally shell-less from about 48 hours thru day 18 in basically a petri dish, but that didn't allow for any evaporation of fluids, and probably minimal on gas exchange as well. otherwise we might have heard more about growing them all the way out in such a way... but everything i could find was more for dissection and study purposes at various stages of embryology and morphology.
that makes sense to me, since 'drowned' chicks usually don't make it much beyond day 18 or 19. If i remember reading, this is because the fluid loaded tissues cause extra strain on the heart, and so basically they die of heart failure due to the extra stresses involved in hatching.
but if it dies of an infection then fluid loss is a moot point. also, with no rigid shell, the membrane is going to move a lot more, and possibly disrupt blood vessel growth needed for gas exchange.
all that said though, while it would require a number of variables to be exactly ON, i don't think it would be impossible. just highly improbable to result in a viable chick. (and probably costly to boot)