Here is the full list of all 45 Carrier Command: Gaea Mission achievements.
Execute Dr. Mao Shin
Shoot down Shin's Manta
Sink the enemy Carrier
Decommission the Geothermal power plants
Run over 100 enemy infantry units
Locate and acquire all available Blueprints
Capture 5 islands without using load
Capture 3 islands without using load
Destroy 100 Walruses using a Manta
Capture 1 island without using load
Destroy 100 Mantas from Direct Control
Rescue Captain Aurora from the APA
Defeat the enemy Carrier in naval combat
Unleash the Lord of Death within you, eliminate Fulcrum's facilities
Destroy 100 Walruses from Direct Control
Locate all Green Laser research files
Reassemble the Hammerhead Nuclear Missile system
Destroy 100 Turrets from Direct Control
Restore contact with Captain Aurora
Locate survivors from the Dead Zone drop
Run over 50 enemy infantry units
Destroy 1 Manta from Direct Control
Destroy 1 Walrus using a Manta
Destroy 1 Walrus from Direct Control
Run over 1 enemy infantry unit
Destroy 1 Turret from Direct Control
Successfully commandeer an enemy Carrier
Capture over 250 islands
Capture the enemy Stockpile
Mine over 1 million in resources
Produce over 1000 items
Capture all enemy islands in the Dead Zone
Capture 1 island with a Strong defense
Capture 10 islands with a Strong defense
Capture 50 islands with a Strong defense
Capture 1 island with a Very Strong defense
Capture 10 islands with a Very Strong defense
Capture 25 islands with a Very Strong defense
Capture 1 island with a Deadly defense
Capture 10 islands with a Deadly defense
Capture 25 islands with a Deadly defense
Destroy 1000 Mantas from Direct Control
Destroy 1000 Walruses from Direct Control
Destroy 1000 Turrets from Direct Control
Destroy 1000 Walruses using a Manta