Here is the full list of all 36 Planet Invasion achievements.
Destroy 50 Murica Missiles
Destroy 250 Murica Missiles
Destroy 500 Murica Missiles
Destroy 1000 Murica Missiles
Destroy 1500 Murica Missiles
Destroy 100 Furious Missiles
Destroy 1000 Furious Missiles
Destroy 2000 Furious Missiles
Destroy 3000 Furious Missiles
Destroy 4000 Furious Missiles
Destroy 50 Vanquisher Missiles
Destroy 500 Vanquisher Missiles
Destroy 1000 Vanquisher Missiles
Destroy 1500 Vanquisher Missiles
Destroy 2000 Vanquisher Missiles
Destroy 25 Judge Missiles
Destroy 250 Judge Missiles
Destroy 500 Judge Missiles
Destroy 750 Judge Missiles
Destroy 1000 Judge Missiles
Unlock Level 4
Unlock Level 7
Unlock Level 10
Unlock Ship 3
Unlock Ship 6
Unlock Ship 9
Unlock Ship 12
Unlock Ship 13
Save 50 alien pods
Save 100 alien pods
Get hit by an asteroid 25 times
Get hit by asteroids 50 times
Use 50 satellites
Use 100 satellites