Here is the full list of all 28 The King's Campaign achievements.
Start the game
Choose your preferred language
Open the Options menu
Open the Campaign menu
Start the king's campaign
Level up one of your Cities
Construct a building in a City from the World Map
Construct walls for your City from the World Map
Train a unit from the World Map
Create a new army
Auto-resolve a battle
Fight a field battle
Fight a siege battle
Fight a naval battle
Capture an enemy city
Loot an enemy city
Raze an enemy city
Place a Call-To-Arms flag on the map
Open the Messages window (Scribe)
Open the Tech research window (Steward)
Open the Armies window (Marshal)
Open the Diplomacy window (Chancellor)
Pause the world map at any point
Exit the game
Start a campaign with Undead Mode enabled
Your historic rival is defeated
Claim the title of Emperor
Unify all of Europe under your rule