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