Farthest i've gotten without cheat was beating black gate guardian using level 2 trap, trapper medal, and diversions level 1.Also with that setup it's possible to beat dwarf guardian of light as he has no ranged units.
Those eggs only give red spiders, and cave spiders, tried alternating them and simply nothing else comes out.
I've tried searching steam forums, and didn't see anything about impossible no-loss. Only impossible with loses, and abusing uncontrollable stack of spiders. If someone managed to do it, definitely didn't brag about it.
I restarted game many times, and best spell i saw was trap. Even if you get phantom it's too weak early on.