Here is the full list of all 40 Sorcerer King achievements.
Win as the Commander
Complete the Campaign
Equip a champion with items in every slot
Defeat a Minor Faction that has sided with the Sorcerer King
Channel the focus of your Magic between Mana, Lore, and Sovereign Skill
Found 5 additional cities in a single game
Destroy one of the Sorcerer King's Strongholds
Complete a Champion Quest to recruit a new Champion to your cause
Slay Aegethon
Reach level 15 with a champion
Play for 15 hours
Ally with a Minor Faction
Use pioneers to upgrade an Outpost
Get a city to level 9
Slay Vetrar
Kill an enemy with a pioneer attack
Win a "predicted defeat" tactical battle
Play for 5 hours
Get a city to level 5
Settle a new city
Use a pioneer to build an Outpost
Reach level 5 with a champion
Craft an item
Claim a Shard
Build your first city improvement
Win a tactical battle
Use the Sovereign's magic to intervene in a tactical battle
Lower the Doomsday Counter
Complete a Quest
Play for 40 hours
Play for 100 hours
Win a "predicted defeat" tactical battle without taking damage
Win 20 "predicted defeat" tactical battles without taking damage
Win a game on Insane Difficulty
Win a game without a single shard destroyed
Win as the Guardian
Win as the Tyrant
Win as the Wizard
Win as the Priest
Win as the Tinkerer