Here is the full list of all 15 Didgery achievements.
Summon Didgery five times
Unlock all Special Cards
Create a chain that includes three special cards
Create a chain consisting of four sevens
Destroy an entire column of cards
Include all four Kings and all four Queens in a single chain
Create a chain that includes more than eight cards
Unlock Nightmare Mode
Unlock your first Forbidden Parchment
Perform your first Holy Explosion
Create 5000 chains
Keep the Earth from descending into Hell for at least 50 mins
Unlock an Artifact using a Didgery Summon
Unlock all Forbidden Parchments
Destroy an entire row of cards