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 100 enemy robots with melee attacks.
Complete all of the Tactical Challenges in VANQUISH.
Destroy 10 enemies distracted by cigarettes during one mission.
Destroy all the floating turrets in Act 3-4.
Destroy the Buzzard without allowing it to reach ground level in Act 5-1.
Find and fire upon all of the Pangloss statues hidden on the colony.
Complete all Acts on Hard difficulty or above.
Complete Act 5 on Hard difficulty or above.
Complete Act 4 on Hard difficulty or above.
Complete Act 3 on Hard difficulty or above.
Destroy five or more enemy transports from atop the Kreon in Act 3-7.
Complete Act 2 on Hard difficulty or above.
Destroy two Argus robots in Act 2-3 while they are in bipedal mode.
Complete Act 1 on Hard difficulty or above.
Revive 20 friendly troops.
Destroy four enemies simultaneously with the Lock-on Laser.
Complete all Acts.
Complete the game without dying, regardless of difficulty level.
Complete Act 5.
Complete Act 4.
Ignore the elevator start order in Act 4-1. Instead, hold position and destroy all reinforcements.
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.
Complete Act 2.
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 at once with rocket launcher splash damage.
Destroy three enemy robots while in damage-triggered AR Mode.
Level a weapon up to maximum operational capability.
Destroy two or more enemy robots at once with the LFE gun.
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.
Maintain a Boost dash to the limit of the ARS reactor without overheating.
Destroy a Romanov with a melee attack.
Destroy a Chicane with a hand grenade.
Complete Act 1.
Scan and acquire all weapons.
Destroy ten enemy robots with melee attacks.
Destroy the arms, head, and back of an KNRB-0 Argus robot.
Destroy ten enemy robots that have been disabled with an EMP emitter.
Revive a friendly troop.
Destroy ten incoming missiles or grenades.
Destroy an incoming missile or grenade.
Destroy three enemy robots at once with one hand grenade.
Manually trigger AR Mode and destroy three enemy robots in a row.
Manually trigger AR Mode and destroy an enemy robot.
Complete all DARPA training exercises.