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