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