Here is the full list of all 45 Nekomew's Nightmares achievements.
My first challenge
Challenges: 10
Challenges: 20
Challenges: 50
Challenges: 100
Total musical notes: 100
Total musical notes: 500
Total musical notes: 1,000
Total musical notes: 5,000
Total musical notes: 10k
Complete a custom level created by a player.
You completed a blocks game level (points).
You completed 7 Nightmare Blocks levels (points).
You completed the "Nightmare Blocks: Mom" level.
You completed a blocks game level (puzzle).
You completed 10 game block levels (puzzle).
You completed the 21 main block game levels (puzzle).
Complete one Cake game level.
Complete 3 Cake Game levels.
You completed the "All invited" Cake Game level.
You completed a basement level.
You completed 10 basement levels.
You completed the 23 main basement levels.
Visit the nightmare "The awakening" wearing the "Dark Nekomew" costume.
Combine 3 blocks in Nightmare Blocks.