Here is the full list of all 46 Sorcerer King: Rivals achievements.
Defeat a Minor Faction that has sided with the Sorcerer King
Craft an item
Settle a new city
Kill an enemy with a pioneer attack
Use the Sovereign's magic to intervene in a tactical battle
Get a city to level 5
Reach level 5 with a champion
Ally with a Minor Faction
Channel the focus of your Magic between Mana, Lore, and Sovereign Skill
Use a pioneer to build an Outpost
Lower the Doomsday Counter
Build your first city improvement
Complete a Quest
Win a tactical battle
Claim a Shard
Play for 5 hours
Play for 15 hours
Play for 40 hours
Play for 100 hours
Complete a Champion Quest to recruit a new Champion to your cause
Equip a champion with items in every slot
Reach level 15 with a champion
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
Win a "predicted defeat" tactical battle
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
Win as Undead
Win as Frozen Realm
Defeat Nabunihr
Defeat Abeix
Defeat Corvos
Achieve Ascension Victory