Here is the full list of all 15 Caverns of Mars: Recharged achievements.
Complete the cavern
Complete all missions
Complete the city and plant the bomb
Complete a level without taking damage
Beat a level without picking up any weapons
Complete the volcano
Destroy 200 Chargers
Destroy 150 Drones
Destroy 175 Kamikazes
Destroy 300 Mines
Destroy 200 Shooters
Destroy 1000 terrain pieces
Destroy 240 Twin Lasers
Drop for 10 seconds without shooting
Use all weapons once