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