Here is the full list of all 50 Vanquish achievements. It takes around 15-20 hours to unlock all of the achievements on Windows.
Find and fire upon all of the Pangloss statues hidden on the colony.
Revive 20 friendly troops.
Destroy 10 enemies distracted by cigarettes during one mission.
Do not allow any friendly armor to be destroyed during Act 3-5.
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 two cannons in Act 3-3 and complete the mission.
Destroy four enemies simultaneously with the Lock-on Laser.
Destroy two Argus robots in Act 2-3 while they are in bipedal mode.
Destroy five or more enemy transports from atop the Kreon in Act 3-7.
Ignore the elevator start order in Act 4-1. Instead, hold position and destroy all reinforcements.
Destroy a Romanov's arms and legs, then finish it with a melee attack.
Destroy a Chicane with a hand grenade.
Complete all of the Tactical Challenges in VANQUISH.
Complete all Acts.
Complete all Acts on Hard difficulty or above.
Complete the game without dying, regardless of difficulty level.
Complete Act 5.
Complete Act 5 on Hard difficulty or above.
Destroy the Buzzard without allowing it to reach ground level in Act 5-1.
Complete Act 4.
Complete Act 4 on Hard difficulty or above.
Destroy the arms, head, and back of an KNRB-0 Argus robot.
Complete Act 3.
Complete Act 3 on Hard difficulty or above.
Destroy 100 enemy robots with melee attacks.
Destroy ten enemy robots that have been disabled with an EMP emitter.
Destroy two or more enemy robots at once with the LFE gun.
Destroy three enemy robots at once with rocket launcher splash damage.
Destroy two Romanovs in a row using only melee attacks.
Defend the Pangloss statue in Act 3-2.
Complete Act 2.
Complete Act 2 on Hard difficulty or above.
Complete Act 1 on Hard difficulty or above.
Manually trigger AR Mode and destroy three enemy robots in a row.
Destroy three enemy robots at once with one hand grenade.
Destroy two enemy robots who have been distracted by a cigarette.
Destroy ten enemy robots with melee attacks.
Level a weapon up to maximum operational capability.
Scan and acquire all weapons.
After taking control of the enemy transport in Act 2-2, do not let a single enemy escape.
Destroy a Romanov with a melee attack.
Complete Act 1.
Destroy ten incoming missiles or grenades.
Destroy three enemy robots while in damage-triggered AR Mode.
Revive a friendly troop.
Maintain a Boost dash to the limit of the ARS reactor without overheating.
Destroy an incoming missile or grenade.
Manually trigger AR Mode and destroy an enemy robot.
Complete all DARPA training exercises.