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

Rochambeau (15 points): Activate a Special Ability.
Come On. Catch Me. (15 points): Earn a Gold, Silver or Bronze Medal on any level.
Couch Potato (10 points): Watch a video clip in the Scrapbook.
White Trasher (20 points): Destroy an enemy with the junkyard crane near Kenny's House.
Space Cash (20 points): Collect 100 coins in 10 seconds or less.
Treasure and Plunder (15 points): Collect 1,000 coins.
Fightin' Round the World (20 points): Throw 1,000 snowballs.
Better than Platinum? (15 points): Earn a Myrrh Medal on any level.
Look For Treasure (5 points): Earn a Platinum Medal on any level.
Ungroundable (20 points): Earn a Bronze Medal or better on 5 Challenge levels.
MANBEARPIG! (20 points): Beat Mountain on Insane difficulty using walls and snowballs. No towers!

Additionally, there is one secret achievement:

Secret achievement (25 points): Unknown.