A Dragonache egg is obtained by digging in a mine using the Diggerling. You then send a Cluckles to the egg to hatch it into a Dragonache. It only worked for me 1 time out of 3 tries, so don't think it will be easy (the Cluckle is pretty stubborn). The egg has to be on a paved surface before the Cluckes will hatch it.