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

Renowned Hero (10 points): Defeat 5 opponents. 
Beast Tamer (10 points): Capture a Mount. 
Warlord (10 points): Win an Xbox LIVE match. 
Knowledgeable Hero (10 points): Research a Spell. 
Ogre Slayer (20 points): Defeat Dugog. 
Bull Slayer (20 points): Defeat Mechataur. 
God Raiser (20 points): Rebuild Sartek. 
Master Engineer (10 points): Complete your citadel. 
Inspiring Leader (15 points): Gain 5 companions. 
Master Craftsman (15 points): Forge a Godlike item. 
Legendary Hero (25 points): Reach Level 50. 
Master of Death (35 points): Defeat Lord Bane.