Here is the full list of all 51 Lunar Flight achievements.
Land & Refuel at Delta - Map1
Land & Refuel at every base on Map1
Land & Refuel at Bravo - Map1
Complete a mission and get the Cockpit Bonus
Land & Refuel at Alpha - Map1
Succesfully land and refuel at a Base other than Alpha
Land & Refuel at Charlie - Map1
Complete a Transport Mission
Purchase an Upgrade
Use an Action Item
Fly off the edge of the map...
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
Acquire Data on a Survey Mission
Complete a Survey Mission
Complete 10 Survey Missions
Complete 10 Transport Missions
Recover a Lost Cargo Container
Complete a Lost Cargo Mission
Complete 10 Lost Cargo Missions
All Upgrades at Level 3
Reach a speed (VEL) of 20 ms then succesfully land at a Base
Complete a Time Trial within the Target Time
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