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