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

88 Miles per Hour (5 points): Travel through time.
Just one hug is enough (5 points): Get a hug from Amy.
Paradise Found (5 points): Complete a zone in the Good Future.
Take the High Road (10 points): Pass the upper Signpost in Collision Chaos Zone 2.
King of the Rings (10 points): Collect 200 Rings.
Statue Saviour (10 points): Find the angel statue in Wacky Workbench.
Heavy Metal (15 points): Defeat Metal Sonic without getting hurt.
All Stages Clear! (15 points): Finish the game.
Treasure Hunter (20 points): Collect all the Time Stones.
Dr. Eggman Got Served (30 points): Destroy Dr. Eggman's final machine.
Just in Time! (35 points): Complete the Time Attack mode in under 25 minutes.
Saviour of the Planet (40 points): Destroy all the robot teleporters and Metal Sonic holograms in the past.