Here is the full list of all 16 Missile Cards achievements.
Prevent 50 hacks
Max out all base upgrades
Get nuked 20 times
Beat all core + bonus missions
Quit 20 matches without playing any cards
Destroy the Final Boss
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Disarm 100 nukes
Lose 25 matches
Collect 250 debris
Win a match with all 4 sub-bases destroyed
Win a match without taking ANY damage
Win a match while clearing the entire deck
Unlock the second base
Win a match with only 1 HP left on your main base