Here is the full list of all 40 Crysis Remastered achievements. It takes around 8-10 hours to unlock all of the achievements on Windows.
Reach the end of 'Onslaught' in the tank you started with
Speed sprint 3km
Tag 30 enemies using the binoculars
Kill an enemy Nanosuit soldier with a Strength punch
Kill 10 enemies by throwing an object at them
Complete 'Core', 'Paradise Lost', 'Exodus' and 'Reckoning' on Delta difficulty
Complete the game on any difficulty
Complete the game on Hard or Delta difficulty
Secure victory in the Battle of Lingshan
Defeat the flight deck invader
Complete all Secondary Objectives
Help the marines evacuate
Escort Prophet to safety
Perform a kill with every firearm
Customize a weapon to use all 5 modification points
Escape the mysterious structure under the mountain
Kill 20 enemies with grab
Complete 'Assault', 'Onslaught' and 'Awakening' on Delta difficulty
Defeat General Kyong
Enter the mines
Proceed to the mining complex
Complete 6 Secondary Objectives
Secure the train station
Destroy 5 enemy tanks
Kill an enemy 200m away
Destroy the cruiser
Destroy all AA guns around the harbor
Kill 400 enemies
Destroy 5 helicopters
Use all weapon attachments
Complete 'Contact', 'Recovery' and 'Relic' on Delta difficulty
Board the VTOL for extraction
Infiltrate the excavation site
Perform 5 consecutive kills without being spotted by an enemy
Complete 3 Secondary Objectives
Kill 200 enemies
Regroup with Prophet upriver
Rescue the hostage
Discover the fate of the Lusca's Call
Pick up an animal