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

God Of War

1.21 Gigawatts (Bronze): Acquire Poseidon's Rage.
Rocking Out (Bronze): Acquire Medusa's Gaze.
Bolt Action (Bronze): Acquire Zeus' Fury.
Sword Man (Bronze): Acquire Blade of Artemis.
Soul Search (Bronze): Acquire Army of Hades.
Matador (Bronze): Win the first Minotaur fight.
Scape Goat (Bronze): Win the first Satyr fight.
Roll Over ... and Die (Bronze): Win the first Cerberus fight.
Don't They Ever Shut Up! (Bronze): Defeat the Desert Sirens.
Beat a Dead Horse (Bronze): Complete the Centaur sacrifice to Hades.
Kickboxer (Bronze): Complete the Spike Room Box Puzzle.
Rockin' the Boat (Bronze): Complete the Sex Mini-Game.
Don't Leave Her Hanging (Bronze): Rescue the Oracle with 10 seconds to spare.
Get the Ball Rolling (Bronze): Complete the Challenge of Atlas.
Totally Baked (Bronze): Complete the Human sacrifice.
Splash (Bronze): Kiss the Nyad.
Get Me a Beer Kid (Bronze): Free yourself from the depths of Hades.
Zero Health = Bronze Trophy (Bronze): Open a Health Chest when your health meter is already full.
Hitman (Bronze): Get a 100 Hits Combo.
Getting My Ass Kicked (Bronze): Die enough times to get offered Easy Mode.
Kratos' Marble Collection (Silver): Collect all the Gorgon Eyes.
Stick it in Your Cap! (Silver): Collect all the Phoenix Feathers.
It's the HUGE One (Silver): Retrieve the Captain's Key.
Take the Bull by the Horns (Silver): Defeat Pandora's Guardian.
God Killer (Silver): Kill Ares.
Head Hunter (Silver): Obtain the head of the Architect's wife.
The Power to Kill a God (Silver): Retrieve Pandora's Box.
Hitman 2 (Silver): Get a 200 Hits Combo.
Legend of the Twins (Silver): Watch the 'Birth of the Beast' Treasure.
Seeing Red (Silver): Max out all Weapons and Magic.
Prepare to be a God (Gold): Beat the Game on any Difficulty.
You Got the Touch! (Gold): Climb the Spiked Column in Hades without taking damage.
I'll Take the Physical Challenge (Gold): Complete the Challenge of the Gods.
Speed of Jason McDonald (Gold): Beat the game in under 5 hours on any Difficulty.
Key to Success (Gold): Collect all of the Muse Keys.
Trophy of Zeus (Platinum): Unlock all God of War Trophies.

God Of War 2

Breaking Wind (Bronze): Acquire Typhon's Bane.
Big, Tuff, Buff and Rough (Bronze): Acquire Rage of the Titans.
Blue Balls (Bronze): Acquire Cronos' Rage.
Shiner (Bronze): Acquire the Golden Fleece.
Rock their World (Bronze): Acquire the Head of Euryale.
Learning to Fly (Bronze): Acquire the Icarus Wings.
Shaky Ground (Bronze): Acquire Atlas Quake.
Death from Above 2009 (Bronze): Defeat the Dark Rider for the first time.
Resurrection (Bronze): Climb from the pit of Hades.
Rock Hard (Bronze): Defeat the Titan Minotaur inside Atlas.
Pick'n on the Little Guy (Bronze): Win the battle outside of the Palace of the Fates.
Watcha Got on the Hot Plate? (Bronze): Solve the riddle of the Fire Phoenix Statue.
Whip it Good (Bronze): Whip the Steeds of Time.
Lift with Your Knees (Bronze): Topple the Temple in the Bog of the Forgotten.
Swinger (Bronze): Cross the collapsing Grapple Bridge.
Stoner (Bronze): Stone and Shatter 30 Enemies.
Super Sized (Bronze): Get a 500 Hits Combo.
Hitting Your Stride (Bronze): Power up any item.
Eye Can't Believe it (Silver): Collect all the Gorgon Eyes.
Go Make a Pillow! (Silver): Collect all the Phoenix Feathers.
Eye Sore (Silver): Collect 20 Cyclops Eyes.
Boss Batch 1 (Silver): Kill the Colossus of Rhodes, the Dark Rider, and Theseus.
Boss Batch 2 (Silver): Kill the Barbarian King, Euryale, and Perseus.
Boss Batch 3 (Silver): Kill the Kraken and all three Sisters of Fate.
Daddy Issues (Silver): Defeat Zeus.
Rise and SHINE (Silver): Awaken the Phoenix.
Spread 'Em (Silver): Open the wings of the Temple of the Fates.
Shine King (Silver): Open the door to the Temple of Euryale.
Blowin' Your Wad (Silver): Max out all Weapons and Magic.
The End Begins (Gold): Beat the Game on any Difficulty.
Feel the Urn (Gold): Collect and use at least 2 Urns of Power.
Bleeding Thumbs (Gold): Beat the Challenge of the Titans.
15 Min Fight Scene (Gold): Battle your way to the Loom Chamber in under 10 minutes.
You Know the Germans Make Good Stuff... (Gold): Collect all Uber Chests.
Trophy of Gaia (Platinum): Unlock all God of War II Trophies.