Accomplish the indicated achievement to get the corresponding number of Gamerscore points:

Big City (5 points): Score a City with 3+ tiles in Single Player.
King of the Road (5 points): Score a road with 5+ tiles in Single Player.
Farm Boy (10 points): Score a Farm supplying 4+ Cities in Single Player.
Rack Up The Points (10 points): Score 50+ points in Single Player.
King For A Day (15 points): Win 1 Ranked game.
Top Score (15 points): Score a total of 2000+ points from all your Carcassonne games combined.
Top Of The Heap (20 points): Win a Player Match against 3 or more opponents.
Count of Carcassonne (20 points): Score 150+ points in a Single Player game.
Metropolis (25 points): Score a City with 9+ tiles in a Player Match vs. 2 or more opponents.
Mirror Monk (25 points): Score 2 adjacent Monasteries in Single Player.
Lord of Carcassonne (25 points): Beat an opponent in a Player Match by 50+ points.
Ultimate Score (25 points): Score a total of 5000+ points from all your Carcassonne games combined.