Here is the full list of all 15 Unpossible achievements.
Score 60 seconds in Daily Futile on 7 different days
Score 60 seconds in Daily Futile on 3 different days
Score 30 seconds in Ultra
Score 60 seconds in Daily Futile
Score 60 seconds in Daily Simplicity
Score 60 seconds in Futile
Score 30 seconds in Futile
Score 30 seconds in Simplicity
Score 60 seconds in Simplicity
Score 60 seconds in Ultra
Score 60 seconds in Daily Futile on 30 different days
Score 60 seconds in Daily Ultra on 3 different days
Score 60 seconds in Daily Ultra on 7 different days
Score 60 seconds in Daily Ultra on 30 different days
Score 60 seconds in Daily Ultra