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

The More I See (5 points): Complete the Tutorials.
Metallica (75 points): Complete any instrument career on Expert (Guitar, Bass, Vocals, Drums or Band).
James Hetfield (25 points): Complete the career as the vocalist.
Lars Ulrich (25 points): Complete the career as the drummer.
Kirk Hammett (25 points): Complete the career as the guitarist.
Robert Trujillo (25 points): Complete the career as the bassist.
Holier Than Thou (150 points): Complete all instrument careers.
One (10 points): Complete a song with any instrument on Hard or Expert in local Quickplay or Career.
...And Justice for All (50 points): Earn 100 stars in Band Career or any single instrument Career.
The Ecstacy of Gold (50 points): Earn $15,000.
Ride the Lightning (10 points): You triggered star power simultaneously (4 player band).
2 X 4 (10 points): Earn a band Hot Streak (4 player band).
Metal Militia (30 points): 100% a song (4 player band).
The Struggle Within (10 points): Complete a song in a band in Quickplay or Career (4 players).
The Four Horsemen (20 points): Complete a song with all band members on expert in Quickplay or Career (4 player band).
Nothing Else Matters (50 points): Complete the career in a band (2-4 player band).
Better Than You (10 points): Win an online Pro Face-Off match.
Blitzkrieg (10 points): Win an online Band v Band match (8 players).
Seek & Destroy (25 points): Play 20 online matches.
The Unforgiven (10 points): Win an online Face-Off match.
Reload (5 points): Download a song from GHTunes.
Hero of the Day (30 points): Complete a song on Expert + in Quickplay or Career (drums only).
Wherever I May Roam (15 points): Complete a song in every venue.
The Memory Remains (5 points): View a Metallifacts video.
Black (10 points): Win an online battle match with the Fade to Black power up.

Additionally, there are 25 secret achievements:

Trapped Under Ice (5 points): You completed a song at the Ice Cave venue.
Lemmy (5 points): You rocked out as Lemmy.
Invisible Kid (5 points): You performed as the bassist.
Some Kind of Monster (5 points): You performed as the guitarist.
The House Jack Built (10 points): You completed a song in every In-the-Round venue.
Astronomy (10 points): You hit every star power phrase in the song Orion.
Stone Dead Forever (5 points): You completed a song at The Stone venue.
Cure (5 points): You recovered from a poor performance in Quickplay or Career.
Eye of the Beholder (5 points): You created a new custom band logo.
Fixxxer (5 points): You created a new custom instrument.
Blackened (5 points): You created a custom tattoo.
Master of Puppets (10 points): You scored the highest individual score on a song in a band.
Disposable Heroes (5 points): You created a new custom rocker.
Damage Inc. (5 points): You performed as the drummer.
Motorbreath (5 points): You performed as the vocalist.
King Diamond (5 points): You rocked out as King Diamond.
Enter Sandman (30 points): You scored 330,000 on the song Enter Sandman on guitar.
Dyer's Eve (30 points): You scored 450,000 on the song Dyer's Eve as the drummer.
Fight Fire with Fire (30 points): You scored 340,000 on the song Fight Fire with Fire as the bassist.
Stone Cold Crazy (30 points): You scored 65,000 on Stone Cold Crazy as the vocalist.
Creeping Death (30 points): You scored 575,000 on the song Creeping Death as the guitarist.
Battery (30 points): You scored 1,000,000 on the song Battery as a band.
The Unforgiven II (10 points): You won an online Face-Off match by 25,000 points or more.
Green Hell (15 points): Drummed every green note and finished the song Blood and Thunder with the rock meter in green.
The Unforgiven III (10 points): You won an online Pro Face-Off match by 25,000 points or more.