When Syrupents have made an egg, watch the egg until it makes 3 bigger hops.
Then tap it with your shovel immediately to get a Twingersnap with fourheads too, but the parents have to be Twingersnaps.

To mature a Dragonache, you have to:
The new hatched Dragonache will be a baby, but won't cocoon on its own
To mature it into an adult, you will need to feed the young Dragonache a bottle of milk, a Snapdragon flower, a Dragumfly, a Reddhott, and a Salamango.
Shortly after eating all five items, the Dragonache will cocoon, then emerge as an adult.