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