Here is the full list of all 8 Vive le Roi achievements.
The first 5 levels are successful
Game completed with at least 1 star for all levels
Game completed with at least 2 stars for all levels
Game completed with at least 3 stars for all levels
The first 10 levels are successful
The first 15 levels are successful
The first 20 levels are successful
The first 25 levels are successful