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