Here is the full list of all 24 VR Apocalypse achievements.
You have completed basic pilot training
You have completed the tutorial
Get 100 kills
Get 1000 kills
Get 5000 kills
Finish Fuel Depot in under 2 minutes
Finish Fuel Depot in under 3 minutes
Finish Fuel Depot in under 1 minute
Shoot over 9000 bullets
Destroy 10 alien nests
Destroy 100 alien nests
Finish Compound in under 2 minutes
Finish Compound in under 4 minutes
Finish Compound in under 3 minutes
Finish Compound in under 1 minute
Finish Bridge in under 2 minutes
Finish Bridge in under 1 minute
Finish Nuclear in under 2 minutes
Finish Nuclear in under 5 minutes
Finish Nuclear in under 4 minute
Finish Nuclear in under 1 minute
Beat the map "Bridge"
Beat the map "Fuel Depot"
Beat the map "Compound"