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

Milk the Cow (10 points): Complete any song (Dance Mode).
It's Electrifying! (10 points): Perform 5 moves in a row with a Perfect rating (Dance Mode).
Greased Lightning (20 points): Achieve a 3 star rating for a Show Your Moves section (Dance Mode).
I Got Chills... (10 points): Achieve a 5 streak (Dance Mode).
...They're Multiplying (20 points): Achieve a 25 streak (Dance Mode).
Dance Fever (20 points): Achieve a x5 multiplier (Dance Mode).
We Go Together (10 points): Complete a song with both a dancer and a singer present (Dance Mode).
Best of Show (20 points): Win 10 rosettes (Challenge Dance Mode).
Unbeatable (10 points): Complete a game without losing or failing any challenges (Challenge Dance Mode).
All The Right Moves (10 points): Pass one of each challenge type (Challenge Dance Mode).
The Zuko (30 points): Complete these moves with a perfect rating - Lightning Arm, Hydromatic Intro, Lasso (Dance Mode).
The Kangaroo Bop (30 points): Complete these moves with a perfect rating - Tell Me More Heart, One I Want, Shaky (Dance Mode).
Greaser (30 points): Complete these moves with a perfect rating - Grease Star, Tiptoe Clicks, Thrust (Dance Mode).
Super Stepper (30 points): Finish a song without performing any poor rated moves (Dance Mode).
Dance Expert (30 points): Finish a song with at least 75% moves rated Perfect (Dance Mode).
National Dance-Off Champion (50 points): Get high scores on all songs (Dance Mode).
Rock and Roll Party Queen (20 points): Complete all songs (Dance Mode).
One For the Yearbook (10 points): Have 20 photos taken of your performance (Dance Mode).
Prom Photo (10 points): Have a photo taken with a friend (Dance Mode).
Something's Begun (10 points): Complete any song (Karaoke Mode).
Vocal Superstar (20 points): Achieve an x5 multiplier (Karaoke Mode).
Tell Me More (10 points): Hit all the spoken word notes in any song that contains them (Karaoke Mode).
Angelic (30 points): Finish a song without performing any poor rated phrases (Karaoke Mode).
Singing Expert (30 points): Finish a song with at least 75% perfect phrases completed (Karaoke Mode).
Hopelessly Devoted (50 points): Post scores to the high score tables for all songs while singing.
Songbird Shake (20 points): Complete all songs (Karaoke Mode).
Full House (10 points): Complete a song with two Dancers and two Singers (Dance Mode).
Oldie But a Goodie (10 points): Unlock a Classic Grease minigame.
Treasure Hunter (20 points): Unlock half the Classic Grease minigames.
Master of Unlocking (20 points): Unlock all the Classic Grease minigames.
Sandy's Songbook (30 points): Unlock all songs (Dance Mode).
Yearbook Yardstick (30 points): Unlock all characters.
Greasy Tom (10 points): Successfully sabotage 3 times in Greasers v Jocks.
All The Way Home (10 points): Hit 5 consecutive home runs in Greasers v jocks.
Basket Case (10 points): Make 5 consecutive baskets in Greasers v Jocks.
On Your Marks (20 points): Complete a race without hitting any hurdles in Run For Your Love.
Road Hodge (10 points): Complete Thunder Road Race without hitting an obstacle.
Let's Get Nuts (10 points): Fully tighten 8 nuts in one playthrough of the Wheel Nuts microgame in Greaser's Garage.
Hit It (10 points): Flatten 3 bumps in a row during Panel Beating in Greaser's Garage without causing any more arising.
Aint No Dropout (10 points): Hit 20 consecutive moves in Beauty Sleep.
Band Leader (10 points): Hit 20 consecutive moves in Rockin’ Rydell.
Gamesmaster (30 points): Complete all the Classic Grease minigames.
T-Bird Trio (30 points): Achieve a score above 250,000 on three Classic Grease minigames.
Buddy Lovin' (30 points): Achieve a team score above 500,000 on three Classic Grease minigames.
Tap It (30 points): Get high scores on all Classic Grease rhythm-action minigames.
Minigame Mogul (50 points): Get high scores on all Classic Grease minigames.
Senior Year Story (10 points): View all story cutscenes.
Rock'n'Roller (30 points): Complete these moves with a perfect rating - Jive Orangutan, Sue, Mid Swing (Dance Mode).

Additionally, there are two secret achievements:

Main Menu Maestro (10 points): Found the main menu Easter Egg.
Rama Lama Ding Dong (10 points): Triggered the Chipmunk Easter Egg in Rockin' Rydell.