Here is the full list of all 51 Lunar Flight achievements.
Land & Refuel at Alpha - Map1
Land & Refuel at every base on Map1
Land & Refuel at Delta - Map1
Land & Refuel at Charlie - Map1
Succesfully land and refuel at a Base other than Alpha
Land & Refuel at Bravo - Map1
The Lunar Module was destroyed
Take off and land at another Base without exceeding an altitude of 10
Reach an altitude of 500 then succesfully land at a Base
Complete a mission and get the Cockpit Bonus
Acquire Data on a Survey Mission
Complete a Survey Mission
Complete 10 Survey Missions
Complete a Transport Mission
Complete 10 Transport Missions
Recover a Lost Cargo Container
Complete a Lost Cargo Mission
Complete 10 Lost Cargo Missions
Purchase an Upgrade
All Upgrades at Level 3
Use an Action Item
Reach a speed (VEL) of 20 ms then succesfully land at a Base
Complete a Time Trial within the Target Time
Fly off the edge of the map...
Land & Refuel at Alpha - Map2
Land & Refuel at Bravo - Map2
Land & Refuel at Charlie - Map2
Land & Refuel at Delta - Map2
Land & Refuel at every base on Map2
Land & Refuel at Alpha - Map3
Land & Refuel at Bravo - Map3
Land & Refuel at Charlie - Map3
Land & Refuel at Delta - Map3
Land & Refuel at every base on Map3
Land & Refuel at every base on all Maps
Load the Mars Map
Land & Refuel at Alpha - Map4
Land & Refuel at Bravo - Map4
Land & Refuel at Charlie - Map4
Land & Refuel at Delta - Map4
Land & Refuel at every base on Map4
Win a Mission Round
Complete a Mission Round
Win a Deathmatch Round
Complete a Deathmatch Round
Get your first kill
Score 10 Kills
Evade a Missile
Evade 10 Missiles
Give some Money
Give 100k in one transaction