Here is the full list of all 50 Vanquish achievements. It takes around 15-20 hours to unlock all of the achievements on Windows.
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.
Complete Act 1.
Destroy ten enemy robots with melee attacks.
Destroy ten incoming missiles or grenades.
Scan and acquire all weapons.
Destroy two enemy robots who have been distracted by a cigarette.
Destroy an incoming missile or grenade.
Destroy three enemy robots while in damage-triggered AR Mode.
Destroy ten enemy robots that have been disabled with an EMP emitter.
Manually trigger AR Mode and destroy three enemy robots in a row.
Destroy three enemy robots at once with one hand grenade.
Revive a friendly troop.
Manually trigger AR Mode and destroy an enemy robot.
Complete all DARPA training exercises.
Complete Act 2.
Complete Act 3.
Complete Act 4.
Complete Act 5.
Complete all Acts.
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.
Level a weapon up to maximum operational capability.
Destroy 100 enemy robots with melee attacks.
Revive 20 friendly troops.
Maintain a Boost dash to the limit of the ARS reactor without overheating.
Destroy a Romanov's arms and legs, then finish it with a melee attack.
Destroy a Romanov with a melee attack.
Destroy two Romanovs in a row using only melee attacks.
Destroy two or more enemy robots at once with the LFE gun.
Destroy three enemy robots at once with rocket launcher splash damage.
Destroy four enemies simultaneously with the Lock-on Laser.
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.
Defend the Pangloss statue in Act 3-2.
Destroy two cannons in Act 3-3 and complete the mission.
Proceed on the monorail in Act 3-4 without being spotted by the enemy troops or searchlights.
Destroy all the floating turrets in Act 3-4.
Do not allow any friendly armor to be destroyed during Act 3-5.
Destroy five or more enemy transports from atop the Kreon in Act 3-7.
Ignore the elevator start order in Act 4-1. Instead, hold position and destroy all reinforcements.
Destroy the Buzzard without allowing it to reach ground level in Act 5-1.
Destroy 10 enemies distracted by cigarettes during one mission.
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.