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

Grime Buster (10 points): Clean up after Fred and George at The Burrow.
Used the Pensieve (10 points): View Dumbledore's first memory of Tom Riddle in the Pensieve.
Quidditch Captain (10 points): Assemble the Gryffindor Quidditch Team.
Great Party (10 points): Create a great Christmas party for Slughorn.
Good Deed (20 points): Help the student retrieve her stolen Gobstone.
Great Mate (20 points): Help Ron avoid Lavender.
Hidden the Book (20 points): Hide the Half-Blood Prince's Potions Book.
Portrait Novice (10 points): Use your first portrait shortcut.
Portrait Pro (20 points): Use all of the portrait shortcuts.
Adventure completed (100 points): Conclude the adventure.
Crest Collector 1 (10 points): Complete Crest Collector Level 1.
Crest Collector 2 (10 points): Complete Crest Collector Level 2.
Crest Collector 3 (10 points): Complete Crest Collector Level 3.
Crest Collector 4 (10 points): Complete Crest Collector Level 4.
Crest Collector 5 (20 points): Complete Crest Collector Level 5.
Crest Collector 6 (20 points): Complete Crest Collector Level 6.
Crest Collector 7 (20 points): Complete Crest Collector Level 7.
Crest Collector 8 (20 points): Complete Crest Collector Level 8.
Crest Collector 9 (30 points): Complete Crest Collector Level 9.
Crest Collector 10 (30 points): Complete Crest Collector Level 10.
Crest Collector 11 (30 points): Complete Crest Collector Level 11.
Crest Collector 12 (40 points): Complete Crest Collector Level 12.
Crest Collector 13 (50 points): Complete Crest Collector Level 13.
Crest Collector 14 (60 points): Complete Crest Collector Level 14.
Potions Beginner (10 points): Earn the Potions Beginner's Luck Badge.
Speedy Brewer Badge (10 points): Earn the Speedy Brewer Badge.
Potions Club Star (10 points): Earn the Potions Club Star Badge.
Potions Club Veteran (20 points): Earn the Potions Club Veteran Badge.
Master Potioneer (50 points): Earn the Master Potioneer Badge.
Duelling Beginner (10 points): Earn the Duelling Beginner's Luck Badge.
Reflex Badge (10 points): Earn the Reflex Badge.
Duelling Champion (10 points): Earn the Duelling Club Champion Badge.
Duelling Veteran (20 points): Earn the Duelling Veteran Badge.
Master Duellist Badge (50 points): Earn the Master Duellist Badge.
Quidditch Beginner (10 points): Earn the Quidditch Beginner's Luck Badge.
Precision Flyer Badge (10 points): Earn the Precision Flyer Badge.
Combo Flyer Badge (10 points): Earn the Combo Flyer Badge.
Keen Flyer Badge (20 points): Earn the Keen Flyer Badge.
Master of Flying (50 points): Earn the Master of Flying Badge.

Additionally, there are four secret achievements, all of which are currently unknown:

Secret achievement (20 points): Unknown.
Secret achievement (20 points): Unknown.
Secret achievement (30 points): Unknown.
Secret achievement (40 points): Unknown.