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