Here is the full list of all 28 Songs of Armageddopolis achievements.
Finished the First Chapter
That was quick, right?
Finished the Third Chapter
Finished the Fourth Chapter
Finished the Fifth Chapter
Trial 1 completed
Trial 1 completed perfectly
Trial 2 completed
Trial 2 completed perfectly
Trial 3 completed
Trial 3 completed perfectly
Trial 4 completed
Trial 4 completed perfectly
Trial 5 completed
Trial 5 completed perfectly
Finished the Last Chapter
Win the match against Berghovski flawlessly
Use your powers to score
Smoke 10 times
Drink a lot of coffee
Choose the right card
Complete the game
You can't play anymore
First time in the Tower
Visit the Tower 3 times
Tower is your second home