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 all the floating turrets in Act 3-4.
Destroy 100 enemy robots with melee attacks.
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 three enemy robots while in damage-triggered AR Mode.
Complete all Acts on Hard difficulty or above.
Complete the game without dying, regardless of difficulty level.
Destroy the Buzzard without allowing it to reach ground level in Act 5-1.
Destroy two Argus robots in Act 2-3 while they are in bipedal mode.
Destroy four enemies simultaneously with the Lock-on Laser.
Complete all of the Tactical Challenges in VANQUISH.
Complete Act 5 on Hard difficulty or above.
Complete Act 4 on Hard difficulty or above.
Complete Act 3 on Hard difficulty or above.
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.
Complete Act 2 on Hard difficulty or above.
Complete Act 1 on Hard difficulty or above.
Complete all Acts.
Complete Act 5.
Complete Act 4.
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.
Manually trigger AR Mode and destroy three enemy robots in a row.
Destroy three enemy robots at once with one hand grenade.
Destroy a Chicane with a hand grenade.
Complete Act 3.
Destroy five or more enemy transports from atop the Kreon in Act 3-7.
Destroy 10 enemies distracted by cigarettes during one mission.
Proceed on the monorail in Act 3-4 without being spotted by the enemy troops or searchlights.
Revive 20 friendly troops.
Destroy three enemy robots at once with rocket launcher splash damage.
Complete Act 2.
Level a weapon up to maximum operational capability.
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 ten enemy robots with melee attacks.
Destroy ten incoming missiles or grenades.
Scan and acquire all weapons.
Destroy a Romanov with a melee attack.
Destroy two or more enemy robots at once with the LFE gun.
Destroy ten enemy robots that have been disabled with an EMP emitter.
Destroy an incoming missile or grenade.
Destroy two enemy robots who have been distracted by a cigarette.
Revive a friendly troop.
Maintain a Boost dash to the limit of the ARS reactor without overheating.
Complete all DARPA training exercises.