Here is the full list of all 18 Crown Champion: Legends of the Arena achievements.
Defeat the champion of Ada's Alehouse.
Defeat the champion of the Temple of Ueres.
Defeat the champion of Greenwood.
Defeat the champion of Sandworth.
Defeat the champion of Waldley.
Defeat the champion of the Dunes.
Defeat the champion of Stonyford.
Defeat the champion of Wainton.
Defeat the champion of Tonstead.
Defeat the champion of Willowsfall.
Pass the trials.
Win the royal tournament.
Build a guard tower on your estate.
Build a bath house on your estate.
Upgrade your main house.
Get married.
Build stables on your estate.
Create a garden on your estate.