Here is the full list of all 51 Vanquish trophies - there are 42 bronze, 5 silver, 3 gold and 1 platinum.
Destroy the Buzzard without allowing it to reach ground level in Act 5-1.
Complete all Acts without using mission select.
Complete Act 5 without using mission select.
Destroy three enemy robots while in damage-triggered AR Mode.
Complete Act 4 without using mission select.
Destroy the arms, legs, head, and back of a KNRB-0 Argus robot.
Ignore the elevator start order in Act 4-1. Instead, hold position and destroy all reinforcements.
Destroy a Romanov with a melee attack.
Complete Act 3 without using mission select.
Destroy five or more enemy transports from atop the Kreon in Act 3-7.
Destroy a Chicane with a hand grenade.
Destroy two enemy robots who have been distracted by a cigarette.
Destroy a Romanov's arm and leg before finishing it.
Level a weapon up to maximum operational capability.
Do not allow any friendly armor to be destroyed during Act 3-5.
Complete Act 2 without using mission select.
Destroy ten enemy robots with melee attacks.
Maintain a Boost dash to the limit of the ARS reactor without overheating.
Destroy ten enemy robots that have been disabled with an EMP emitter.
After taking control of the enemy transport in Act 2-2, do not let a single enemy escape.
Complete Act 1 without using mission select.
Revive 20 friendly troops.
Destroy three enemy robots at once with rocket launcher splash damage.
Destroy two or more enemy robots at once with the LFE gun.
Scan and acquire all weapons.
Manually trigger AR Mode and destroy an enemy robot.
Destroy three enemy robots at once with one hand grenade.
Destroy ten incoming missiles or grenades.
Destroy an incoming missile or grenade.
Revive a friendly troop.
Complete all DARPA training exercises.
Acquire All Trophies
Complete Act 1 on Hard difficulty or above without using mission select.
Complete Act 2 on Hard difficulty or above without using mission select.
Complete Act 3 on Hard difficulty or above without using mission select.
Complete Act 4 on Hard difficulty or above without using mission select.
Complete Act 5 on Hard difficulty or above without using mission select.
Complete all Acts on Hard difficulty or above without using mission select.
Manually trigger AR Mode and destroy three enemy robots in a row.
Destroy 100 enemy robots with melee attacks.
Destroy two Romanovs in a row using only melee attacks.
Destroy four enemies simultaneously with the Lock-on Laser.
Destroy two Argus robots in Act 2-3 while they are in bipedal mode.
Defend the Pangloss statue in Act 3-2.
Destroy two cannons in Act 3-3 and complete the mission.
Proceed on the monorail in Act 3-4 without being spotted by the enemy troops or searchlights.
Destroy all the floating turrets in Act 3-4.
Destroy 10 enemies distracted by cigarettes during one mission.
Find and fire upon all of the Pangloss statues hidden on the colony.
Complete all of the Tactical Challenges in VANQUISH.
Complete the game without dying, regardless of difficulty level.