Here is the full list of all 40 Crysis achievements worth 1,000 gamerscore. It takes around 15-20 hours to unlock all of the achievements on Xbox 360.
Tag 30 enemies using the binoculars
Complete the game on Hard or Delta difficulty
Complete 'Core', 'Paradise Lost', 'Exodus' and 'Reckoning' on Delta difficulty
Complete 'Assault', 'Onslaught' and 'Awakening' on Delta difficulty
Complete all Secondary Objectives
Complete 'Contact', 'Recovery' and 'Relic' on Delta difficulty
Use all weapon attachments
Complete the game on any difficulty
Secure victory in the Battle of Lingshan
Defeat the flight deck invader
Help the marines evacuate
Rescue the hostage
Regroup with Prophet upriver
Infiltrate the excavation site
Board the VTOL for extraction
Destroy all AA guns around the harbor
Destroy the cruiser
Secure the train station
Proceed to the mining complex
Reach the end of 'Onslaught' in the tank you started with
Enter the mines
Defeat General Kyong
Escape the mysterious structure under the mountain
Complete 3 Secondary Objectives
Complete 6 Secondary Objectives
Destroy 5 helicopters
Destroy 5 enemy tanks
Kill 200 enemies
Kill an enemy 200m away
Perform a kill with every firearm
Kill 20 enemies with grab
Speed sprint 3km
Kill an enemy Nanosuit soldier with a Strength punch
Kill 10 enemies by throwing an object at them
Customize a weapon to use all 5 modification points
Kill 400 enemies
Escort Prophet to safety
Discover the fate of the Lusca's Call
Pick up an animal
Perform 5 consecutive kills without being spotted by an enemy