Here is the full list of all 18 Snake Core achievements.
Complete an Attack mission
Complete a Recruit mission
Complete a Protect mission
Complete a Bomb-squad mission
Complete a Survival mission
Complete an Infection mission
Complete a Hunt mission
Complete a Transport mission
Complete Boss Fight mission
Complete Attack mission in Hard mode
Complete Regroup mission in Hard mode
Complete Protect mission in Hard mode
Complete Bomb Squad mission in Hard mode
Complete Survival mission in Hard mode
Complete Hunt mission in Hard mode
Complete Infection mission in Hard mode
Complete Transport mission in Hard mode
Complete Boss Fight mission in Hard mode