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

Man Up! (0 points): Defeat someone over Xbox LIVE who has earned the Man Up! achievement.
First Strike (5 points): Be the first to get an objective in game.
Destroyer (10 points): Kill 100 human, cat, robot, yeti and zombie units.
Faction Specialist (10 points): Complete the human, cat, robot, yeti and zombie campaigns.
Capitalize This (20 points): Control 5 capitals.
Ironman (20 points): Defend a minimum of 5 attackers with one defender.
Demon Child (30 points): Achieve 10 super overkills.
Star Command (30 points): Earn 10 stars and trade them for 30 troops.
Soldier (10 points): Play 5 games on Xbox LIVE.
Master & Commander (15 points): Win a 5 player ranked Command Room game on Xbox LIVE.
Glory Hunter (20 points): Win 10 ranked games on Xbox LIVE.

Additionally, there is one secret achievement:

5 Star General (30 points): You have won a game on each map in custom game.