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

Stone Cold Crash (15 points): Stun 5 Ratcicles as Crash.
Ice On The Cake (20 points): Fully upgrade Ratcicle.
Snow Blows (15 points): Beat all 10 levels of arena minigame in Ratcicle Kingdom.
Spike the Punch (20 points): Stun 5 Spikes as Crash.
Chuck Is That You? (35 points): Score a 20x mojo multiplier via combat combos.
Girl Power (25 points): Beat Coco Boss Fight.
Big Shooter (10 points): Fire a large projectile from the mask in coop mode.
Can U Dig It? (5 points): Enter an underground space.
Slap on the Wrist (20 points): Destroy 75 Slap-E robo-hands.
Happy To See Me (5 points): Store a Mutant in your pocket.
Oo Oo Ah Ah (20 points): Defeat 75 Doom Monkeys.
Goo Squared (20 points): Fully Upgrade Sludge.
Fashion Fury (20 points): Defeat 75 Brat Girls.
Shell Shocked (20 points): Fully upgrade Magmadon.
Lark In The Dark (15 points): Beat all 10 levels of arena minigame in Mount Grimly.
Over Easy (15 points): Complete co-op balancing puzzle in Mount Grimly.
Shoot the Works (20 points): Fully upgrade Snipe.
A Combo to Go (35 points): Defeat 50 enemies in co-op mode.
Crash Grab (50 points): Collect all Crash voodoo dolls.
Break Them To It Gently (25 points): 15x combo scored.
Whack-A-Nerd (20 points): Defeat 75 Ratnicians.
Easy Does It (15 points): Complete co-op balancing puzzle in Wumpa Island above the waterfall.
Follow Your Nose (25 points): Stun 5 Sludges As Crash.
Hot Stuff (25 points): Collect all Wasteland voodoo dolls.
No Place Like Wumpa (25 points): Collect all Wumpa voodoo dolls.
Multi-Tasking (5 points): Store a Mutant while riding another one.
Glass Is Half Full (50 points): Complete 50% of the game.
Stand in the Sand (15 points): Beat all 10 levels of arena minigame in Wasteland.
Shadow Boxing (20 points): Defeat 75 Znu.
P Stinking U! (20 points): Fully Upgrade Stench.
N Is For Evil (25 points): Collect all evil school voodoo dolls.
Freezer Burn (25 points): Collect all Ice voodoo dolls.
Night Fright (20 points): Fully upgrade Grimly.
A Wumpa A Day (15 points): Find a Crash health upgrade collectible.
Roll It Up! (20 points): Fully upgrade RhinoRoller.
Neo Is Getting Angry (50 points): Beat Cortex Boss Fight.
It Took Two To Tango (15 points): Complete coop balancing puzzle in the Wasteland.
Crash King (25 points): Fully upgrade Crash.
Duplex Crash (10 points): Defeat 1 enemy in coop mode.
T to the K (20 points): Fully upgrade TK.
The Dark Side (25 points): Collect all Mount Grimly voodoo dolls.
Would You Like Fries With That? (10 points): Score a 10x mojo multiplier via combat combos.
Crunched (25 points): Beat Crunch Boss Fight.
Don't Recycle (25 points): Collect all Junkyard voodoo dolls.

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

Secret achievement (15 points): Unknown.
Secret achievement (10 points): Unknown.
Secret achievement (15 points): Unknown.
Secret achievement (20 points): Unknown.