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