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

Whumpa Warrior (15 points): Complete All Whumpa Island Episodes.
Goose Goose Duck! (10 points): Jack A Yuktopus.
Temple Of Boom (10 points): Complete Temple Episode.
Harder They Fall (15 points): Complete All Lumber Yard Episodes.
Tiny Detour (10 points): Complete Lava Episode.
Beach Blanket Bombardment (15 points): Complete All Beach Episodes.
Facts of Strife (15 points): Complete All Factory Episodes.
All Bark, No Might (10 points): Jack Uka Uka.
Barking Up The Wronged Tree (25 points): Complete All Uka Tree Episodes.
Sticky Fingers (15 points): Jack Nina's Arachnina.
Courting Catastrophe (25 points): Complete All Cortex Lair Episodes.
Gold Digger (15 points): Earn 1 Gold Episode Idol.
Mojo Magic (10 points): Complete 1 Mojo Room Challenge.
Five By Five (10 points): Accrue 5 Extra Lives.
Easy Pickings (15 points): Collect 5 Hidden Idols.
Ringer (15 points): Earn 5 Gold Episode Idols.
Soaking In It (25 points): Unlock 5 Creature Costume Idols.
Like A Cat (20 points): Accrue 9 Extra Lives.
Mojo Mania (15 points): Complete 10 Mojo Room Challenges.
Stayin' Alive (30 points): Accrue 15 Extra Lives.
Crate Crazy (20 points): Smash 100 Crates Of Any Scale.
Aiming To Please (20 points): Jack 20 Projectile Creatures By Any Means.
Brutal Buffet (35 points): Jack 5 Of Every Type Of Jackable Creature.
Baker's Dozen (13 points): Jack 13 Strongs By Any Means.
Carry A Bigger Stick (15 points): Jack 5 Captains By Any Means.
Duplex Planet (20 points): Play Co-Op.
Fits Like A Glove (10 points): Unlock 1 Creature Costume Idol.
Gimme Some Skin (26 points): Unlock 10 Creature Costume Idols.
Midas Touch (25 points): Earn 10 Gold Episode Idols.
Master At Harms (25 points): Defeat 200 Minion Fodder.
Mojophoria! (25 points): Complete All Mojo Room Challenges.
Treasure Hunter (25 points): Collect All 20 Hidden Idols.
Sampler Pack (30 points): Jack 1 Of Every Type Of Jackable Creature.
Monster Whisperer (30 points): Jack 75 Strong Creatures.
Self-Help Guru (15 points): Fully Upgrade Crash's Health.
Mojofied (30 points): Unlock & Upgrade All Crash's Abilities.
Master Of Disguise (36 points): Unlock All Creature Costume Skins.
JACK KING (75 points): Complete 100% of the Game.
Alive & Kicking (10 points): Complete All Episodes on Hard.
Over Easy (25 points): Earn Gold for All Episodes on Easy.
Medium Rare (35 points): Earn Gold for All Episodes on Medium.
Hard Knocks (60 points): Earn Gold for All Episodes on Hard.

Additionally, there are five secret achievements:

Right Stuff (5 points): Free fall for 5 seconds.
Big Spender (10 points): 9 Lives spent in a single episode.
Idle Hands (15 points): Let Crash do 10 funny things.
Eavesdropper (20 points): Five creature conversations heard through.
Where Did The Time Go? (25 points): Spent longer than 25 minutes in a single episode.

Big head Crash - Pause the game, then hold RT and press X(2), Y, A. Keep RT held until the game is resumed. Repeat the code to disable its effect.

Invisible Crash - Pause the game, then hold RT and press Y, X, Y, A. Keep RT held until the game is resumed. Repeat the code to disable its effect.

Skins - Successfully complete the indicated task to unlock the corresponding skin for Crash:

Battler: Jack 35 Battlers.
Bratgirl: Defeat 130 Brat Girls.

Doom Monkey: Defeat 500 Doom Monkeys.

EE-Lectric: Jack 50 EE-Lectrics.

Goar: Jack 30 Goars.

Halloween: Successfully complete 50% of the game.

Koo-ala: Defeat 150 Koo-Alas.

Magmadon: Jack 50 Magmadons.

Ratnician: Defeat 200 Ratnicians.
Rhinoroller: Jack 30 Rhinorollers.

Scorporilla: Jack 15 Scorporillas.
Shellephant: Jack 15 Shellephants.
Sludge: Jack 50 Sludges.
Snipe: Jack 50 Snipes.
Spike: Jack 50 Spikes.
Stench: Jack 50 Stenches.

Valentine: Collect all Gold Idols.
Voodoo Bunnie: Defeat 200 Voodoo Bunnies.

Easy jacks - Wear a skin that matches the creature to be jacked. A single hit will knock it out, allowing it to be jacked easily.