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