Here is the full list of all 17 They Are Coming! achievements.
Finish the game in storm mode.
Complete the 14th stage.
Complete the 13th stage.
Complete the 12th stage.
Complete the 11th stage.
Complete the 10th stage.
Complete the 9th stage.
Complete the 8th stage.
Reach SSS rank at any stage.
Complete the 7th stage.
Complete the 6th stage.
Complete the 5th stage.
Complete the 4th stage.
Complete the 3rd stage.
Complete the 2nd stage.
Complete the 1st stage.
Complete the tutorial