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