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