Here is the full list of all 20 The Solitaire Conspiracy achievements. It takes around 4-5 hours to unlock all of the achievements on Windows.
Get to Wave 15 in Countdown
Get to Wave 10 in Countdown
Complete the Campaign
Complete Level 13
Complete Level 12
Complete Level 11
Complete Level 10
Get to Wave 5 in Countdown
Complete Level 9
Complete Level 8
Complete Level 7
Complete a Skirmish with four crews
Complete a Skirmish with only one crew
Complete Level 6
Complete Level 5
Complete Level 4
Complete Level 3
Complete Level 2
Change the game's color theme for the first time
Complete Level 1