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