Here is the full list of all 20 Days Like A Nightmare achievements.
Clear DAY3 NIGHTMARE
Clear DAY2 NIGHTMARE
Clear DAY1 NIGHTMARE
See the Secret Ending
Clear DAY6
Clear DAY5
Shoot Something You Shouldn't
Clear DAY4
Clear DAY3
Clear DAY2
Clear DAY1
Clear DAY1 HARD
Clear DAY2 HARD
Clear DAY3 HARD
Clear DAY4 HARD
Clear DAY5 HARD
Clear DAY6 HARD
Clear DAY4 NIGHTMARE
Clear DAY5 NIGHTMARE
Clear DAY6 NIGHTMARE