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

Centurion (10 points): Get 100 or more rings. 
Clear Green (5 points): Clear the Green Hill Zone. 
Fast Green (10 points): Beat Green Hill Zone Act 1 in under 35 seconds. 
Fast Marble (15 points): Beat Marble Zone Act 1 in under 80 seconds. 
Star Light Zone (5 points): Get to the Star Light Zone. 
Spring Yard Zone (7 points): Get to the Spring Yard Zone. 
Labyrinth Zone (8 points): Get to the Labyrinth Zone. 
Chaos Emerald (10 points): Get one Chaos Emerald. 
Chaos Master (35 points): Get all the Chaos Emeralds. 
Win (25 points): Beat the game. 
Fast Win (30 points): Beat the game in under 40 minutes. 
Perfect Win (40 points): Beat the game without dying.