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