This game has 51 trophies that can be collected.

Bronze

One Day at DARPA
Complete all DARPA training exercises.

Space Normandy
Complete Act 1.

Storming Grand Hill
Complete Act 2.

I Don't Speak Kreon!
Complete Act 3.

My Way
Complete Act 4.

End to Major Combat Operations
Complete Act 5.

Operation Overlord II
Complete Act 1 on Hard difficulty or above.

Ain't Life Grand?
Complete Act 2 on Hard difficulty or above.

Cry on, Kreon!
Complete Act 3 on Hard difficulty or above.

The High Way
Complete Act 4 on Hard difficulty or above.

Mission Accomplished
Complete Act 5 on Hard difficulty or above.

Gun Runner
Scan and acquire all weapons.

King of the Hill
Level a weapon up to maximum operational capability.

Fight or Flight
Manually trigger AR Mode and destroy an enemy robot.

Adrenaline Rush
Manually trigger AR Mode and destroy three enemy robots in a row.

Going in for the Kill
Destroy two enemy robots with melee attacks.

Helloooo, Nurse
Revive a friendly troop.

Knight in Shining White Armor
Revive 20 friendly troops.

Death Wish
Destroy three enemy robots while in damage-triggered AR Mode.

40 Yard Dash
Maintain a Boost dash to the limit of the ARS reactor without overheating.

Home Run
Destroy an incoming missile or grenade.

Home Run God
Destroy ten incoming missiles or grenades.

Brutality Bonus
Destroy a Romanov's arms and legs, then finish it with a melee attack.

Romanov This!
Destroy a Romanov with a melee attack.

Robots Tend to Blow Up
Destroy three enemy robots at once with one hand grenade.

Hole-in-One
Destroy a Chicane with a hand grenade.

Short Circuit
Destroy ten enemy robots that have been disabled with an EMP emitter.

Two Birds with One Stone
Destroy two or more enemy robots at once with the LFE gun.

Trick Shot
Destroy three enemy robots at once with rocket launcher splash damage.

Piece by Piece
Destroy the arms, head, and back of an KNRB-0 Argus robot.

That Ended Up Working Nicely
After taking control of the enemy transport in Act 2-2, do not let a single enemy escape.

Failure Breeds Success
Destroy two Argus robots in Act 2-3 while they are in bipedal mode.

Leibniz Defense Agency
Defend the Pangloss statue in Act 3-2.

Tightrope Walker
Destroy two cannons in Act 3-3 and complete the mission.

Fisher is the Other Sam
Proceed on the monorail in Act 3-4 without being spotted by the enemy troops or searchlights.

Flyswatter
Destroy all the floating turrets in Act 3-4.

Guardian
Do not allow any friendly armor to be destroyed during Act 3-5.

Hurry the #@$% Up!
Destroy five or more enemy transports from atop the Kreon in Act 3-7.

Civil Disobedience
Ignore the elevator start order in Act 4-1. Instead, hold position and destroy all reinforcements.

Buzzard Beater
Destroy the Buzzard without allowing it to reach ground level in Act 5-1.

Smoke 'em if ya got 'em!
Destroy 10 enemies distracted by cigarettes during one mission.

Auld Land Syne
Destroy two enemy robots who have been distracted by a cigarette.

Silver

Survivor
Complete all Acts.

A Heartbreaker and Lifetaker
Destroy 100 enemy robots with melee attacks.

The Hand of God
Destroy two Romanovs in a row using only melee attacks.

Flash! King of the Impossible
Destroy four enemies simultaneously with the Lock-on Laser.

The Best of All Possible Worlds
Find and fire open all of the Pangloss statues hidden on the colony.

Gold

ARS Operator
Complete all Acts on hard difficulty or above.

Legend
Complete the game without dying, regardless of difficulty level.

Platinum

Platinum
Earn all available trophies in VANQUISH.

1 Secret

http://www.ps3trophies.com/forums/trophy-news/45054-vanquish-trophy-list.html