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