Here is the full list of all 16 8-Bit Bayonetta achievements. It takes around 0-1 hour to unlock all of the achievements on Windows.
Finish with a score between 8000 and 13000
Reach a score of 5000
Maintain a very high rate of fire
Fire 1000 bullets
Killed by a land angel
Launch the game multiple times
Single jump 30 times
Try again
Double Jump lots during a game
Kill a land angel
Killed by a flying angel
Die without scoring
Dodge multiple axe attacks in 1 game
Reach a score of 13000 or more
Finish with a very specific score
Kill a lot of angels