Classic Wolverine (blue/yellow) costume - While playing the game, press X, Square, Circle, X, Triangle, X, Triangle, X, Square, Circle(2), Square, R3 to unlock Wolverine's classic blue and yellow costume. If you entered the code correctly, you will hear a sound. Then, exit to the main menu, and switch costumes.

3D mode - Successfully complete the game on the Hard difficulty to unlock 3D mode.

Hard mode - Successfully complete the game to unlock the Hard difficulty.

Alternate costumes - Successfully complete the indicated task to unlock the corresponding costume:

Classic Wolverine (blue/yellow): Collect the two action figures of Classic Wolverine. Then, defeat Classic Wolverine in his challenge.
Legendary Wolverine (brown/yellow): Collect the two action figures of Legendary Wolverine. Then, defeat Legendary Wolverine in his challenge.
X-Force Wolverine: Collect the two action figures of X-Force Wolverine. Then, defeat X-Force Wolverine in his challenge.

Easy "Found!" trophy - After you crash the jeep on the first level and continue, you will reach an area with a barricaded gate. Climb over the rocks, and go in. Defeat the enemies. Look for some boards over a small doorway off on one of the areas. Slice them up, and enter to find the hatch on the ground near the back corner and get the "Found!" trophy.

Easy "The Cake" trophy - There is a part in the Sentinel factory where you must freeze yourself to get past a heat detector. Move a teleporter all the way to the right. It will go through the wall and enter a secret room. Teleport there to collect the cake that is inside and get "The Cake" trophy.

Easy "WoW!" trophy - Go to the Alkali Lake section of the Frozen Tundra (before the Agent Zero fight). Immediately after the long road section with the shield troops is a fallen tree. Enter the forest that leads to a cave. Inside will be the sword and skeleton.

Trophies - Successfully complete one of the following tasks to get a trophy:

Getting Started (Bronze): Killed 100 enemies.
A Day's Work (Bronze): Killed 500 enemies.
You Can't Hide (Bronze): Lunged to 250 enemies.
Lunge (Bronze): Lunged to 25 enemies.
Pounce (Bronze): Lunged to 100 enemies.
Piggy Back Ride (Bronze): Lunged to a W.E.N.D.I.G.0 prototype's back.
Quick Killer (Bronze): Quick Killed 1 enemy.
Efficient Killer (Bronze): Quick Killed 20 enemies.
Perfect Killer (Bronze): Quick Killed 3 enemies in a row.
Drop Dead (Bronze): Killed 10 enemies by throwing them off high areas.
Apprentice (Bronze): Raised One Combat Reflex to Master Level.
Mutant Lover (Bronze): Raised one Mutagen to level 3.
Astonishing (Bronze): Found 1/2 of all Dog Tags in the game.
Defensive (Bronze): Performed 1 Counter move.
Untouchable (Bronze): Performed 25 Counter moves.
Catch! (Bronze): Killed 1 enemy with a reflected projectile.
Boomerang (Bronze): Killed 25 enemies with a reflected projectile.
Aerial Assault (Bronze): Performed 10 Air Grabs.
Ultimate Wolverine (Bronze): Fought 4 W.E.N.D.I.G.0 prototypes at the same time and defeated them at Alkali lake..
Hot Potato (Bronze): Light 20 enemies on fire.
Shotgun Epic Fail (Bronze): Killed 25 Ghosts with their own weapon.
WoW! (Bronze): You feel a cold as you examine the sword and skeleton. A rustle of wind in the trees faintly echoes the name Arthas.
Aerial Master (Bronze): Got 6 enemies airborne at once.
Fully Loaded (Bronze): Maxed out all upgrades.
Slice n' Dice (Bronze): Killed 6 enemies with a single attack.
Found! (Bronze): You found a mysterious hatch!.
Slaughter House (Bronze): Dismembered 100 enemies.
Heightened Senses (Bronze): Killed 200 enemies in Feral Sense.
Environmentally Friendly (Bronze): Killed 10 enemies using objects in the environment.
Whatever it Takes (Bronze): Killed 30 enemies using objects in the environment.
Bloodlust (Bronze): Killed 50 enemies while in Berserker mode.
Weapon X (Bronze): Killed 150 enemies while in Berserker mode.
The Cake (Bronze): You found the cake, yummy!.
Clean Up on all Aisles (Bronze): Destroyed all objects in the grocery store fight with Fred Dukes (The Blob).
What I Do Best (Silver): Killed 2000 enemies.
Samurai (Silver): Raised All Combat Reflexes to Master Level.
Devil's Brigade (Silver): Found all Dog Tags in the game.
Blender (Silver): Killed 200 enemies with Claw Spin.
Walking Death (Gold): Beat the game on Hard Difficulty.

Additionally, there are twelve secret trophies:

Spillway Escape (Bronze): Escapes from Weapon X.
Threading the Needle (Bronze): Flew through the O ring in the Sentinel Boss Battle.
James Howlett (Bronze): Performed a Wolverine to Wolverine Lunge.
Stick Around (Bronze): Impaled Victor Creed outside the Bar.
Bar Fight (Silver): Defeated Victor Creed (Sabretooth).
Helicopter Ride (Silver): Defeated David Nord (Agent Zero).
Fallen Sentinel (Silver): Defeated the Sentinel Mark I.
Put up your Dukes (Silver): Defeated Fred Dukes (The Blob).
52 Pickup (Silver): Defeated Remy LeBeau (Gambit).
The Village (Silver): Completed the Jungle Mission.
The Dead Pool (Gold): Defeated Weapon 11 (Deadpool).
Platinum (Platinum): You collected all the trophies in Wolverine.