Here is the full list of all 28 Alekhine's Gun achievements.
Complete all assassinations in a level using only accidents
Obtain Ghost Ranking on a level
Obtain Maniac Ranking on a level
Complete level 11
Complete the game without killing except for assassination targets
Complete level 10
Complete level 9
Complete level 8
Complete level 7
Perform a perfect rewiring during a sabotage puzzle
Complete level 6
Complete level 5
Perfect lockpicking attempt on a lock with at least 4 locking mechanisms
Complete level 4
Complete level 3
Complete a level without using your gun
Complete level 2
Complete level 1
Complete a level using one disguise or less
Complete a level without killing except for assassination targets
Complete a level without using Instinct Mode
Get 30 Headshots
Use chloroform on 30 enemies
Garrote 30 enemies
Obtain all disguises in the game
Hide 30 bodies
Obtain Ghost Ranking on all levels
Obtain all trophies