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

Funchucks! (15 points): Recover the Funchucks in Hong Kong.
Bad Axes! (15 points): Acquire The Bad Axes.
Blast Caster! (15 points): Acquire The Blast Caster.
Agent Of Providence (60 points): Finish The Campaign.
Nanite Hacker (15 points): Gather All Computer Info From Dr. Rylander's Lab.
Memories (15 points): Get The First Item Of Rex's Past.
Get Your Scrapbook Ready (30 points): Collect All Items Of Rex's Past.
First Step To The Date (15 points): Collect The 1st Sample For Doctor Holiday.
Impressing Doctor Holiday (15 points): Collect All The Samples Of Any 2 EVOs.
Date With Doc (30 points): Collect All The Samples For Doctor Holiday.
Getting Stronger... (15 points): Purchase An Upgrade.
Master Of Machines (20 points): Purchase All Upgrades.
All Boxed Up (15 points): Open 30 Supply Boxes.
Bleach Protocol (15 points): Defeat 200 Enemies.
Feeling Punchy? (30 points): Defeat 100 Enemies With The Smack Hands.
Slice N' Dice (30 points): Defeat 100 Enemies With The BFS.
Blaster Master (30 points): Defeat 100 Enemies With The Slam Cannon.
Bustin' Some Punks (30 points): Defeat 100 Enemies With The Punk Busters.
M. Rex (15 points): Defeat 100 Enemies With Omega Builds.
Killer Combo (15 points): Get A 20 Hit Combo.
Ultra Combo (60 points): Get A 60 Hit Combo.
Too Easy (15 points): Beat One Agent Six Time Challenge Level.
Call That A Challenge? (30 points): Beat Any One Agent Six Time Challenge In Under 10 Mins.
Better Than Six (60 points): Beat All Agent Six Time Challenges.
And Away They Go! (15 points): Knock 20 EVOs Out Of The World.
Human Bullet (40 points): Collect All The Nanites And Do Not Get Hurt In Sky Diving.
Radical Rex Ride! (40 points): Kill All EVOs And Take No Damage In Rex Ride.
Collateral Damage (20 points): Indirectly Defeat 30 EVOs.
Escape Artist (15 points): Successfully Wiggle Free Of 20 Spider Webs Without Taking Damage.

Additionally, there are 15 secret achievements:

Rev Your Engine! (15 points): Completed The Rex Ride Sequence.
Omega Victory (15 points): Defeated Giant Van Kleiss.
Out Of Pocket (15 points): Defeated Breach.
Deep Sea Rescue (15 points): Cured Aquania.
I Hate That Bunny (15 points): Defeated The EVO Death Bunny.
Not Just A Pretty Face (15 points): Solved The Puzzle In The Temple.
U-G-L-Y... (15 points): Defeated The Multi-Head EVO.
Threading The Needle (15 points): Successfully Flew Through The Circular Debris While Sky Diving.
Training Complete (15 points): Completed The Tutorial In Mexico.
Circe... (15 points): Encountered Circe.
Big Bad Wolf (15 points): Defeated Biowulf.
Van Kleiss! (15 points): Defeated Van Kleiss In Providence.
Damsel In Distress (15 points): Saved Doctor Holiday.
Stone Cutter (40 points): Beat Quarry In 2.5 Mins. Or Less.
Flawless Victory (30 points): Defeated Van Kleiss In Abysus Castle Without Taking Any Damage.