Here is the full list of all 40 Dark Deity achievements.
Acquire all other achievements
Have all stats increase on a single levelup
Beat the game on Deity mode
Prove your worth to King Varic in under 8 turns
Chapter 1: Get drafted
Eat corn with Benji
Have a unit take 150 damage and live in one chapter
Beat the game
Beat the game on Mortal mode
Beat the game on Hero mode
Chapter 27: Find the resolve to continue on
Chapter 25: Defeat one of your greatest enemies
Deploy 6 mounted units at once
Chapter 23: Resolve some long running familial tension
Chapter 20: Chase a dangerous foe away
Upgrade a unit to tier 3
Promote a character into the tier 3 corresponding to their tier 2
Chapter 16: Defeat a legendary creature
Upgrade all of a unit's weapons to tier 4
Have a character move 150 tiles in a chapter
Take 25 or more turns to clear a chapter
Chapter 15: Complete the Trial of Soul
Have a single unit dodge 20 or more times in one chapter
Defeat 15 enemies with one unit in a single chapter
Reach the max level of a single spell/weapon tree
Clear Chapter 12 while the boat is below 30 health
Reach a max level bond
Chapter 12: Leave Etlan by way of sea
Chapter 11: Complete your most harrowing battle yet
Clear a chapter with Thae'Lanel, Corvan, or Maeve as your MVP
Start a chapter with aspects equipped to every deployed unit
Chapter 8: Have someone close to you witness a shameful act
Clear Chapter 7 while the aqueducts are over 50 health
Chapter 5: Defeat the onslaught of undead
Upgrade a unit to tier 2
Defeat an enemy in one hit.
Upgrade your first spell/weapon
Take 0 damage from an attack.
Get a critical hit
Have one unit take 50% of the team's damage in a chapter