Here is the full list of all 35 HENTAI PUZZLE achievements.
Couchtime
Start a new game with progress of a least 5 completed puzzles
Click a tiny dick 10000 times
Click a tiny dick 9001 times
Click a tiny dick 5000 times
Click a tiny dick 1000 times
Click a tiny dick 500 times
Click a tiny dick 200 times
Click a tiny dick 100 times
Click a tiny dick 50 times
Click a tiny dick 20 times
Click a tiny dick 10 times
You noticed you have a small dick to play with
Click a tiny dick 5 times
Complete the game
Sticky Eggplant
What a mouthful
Hands On
Get over here
Slowly pressed against the glass
Skip the story dialogs 200 times
Click *yourself* back to the menu
Sushi???
Complete 5 Puzzles
Pressed against the glass
Complete the cow puzzle
Complete the second second puzzle
Click the hint button 30 times
Complete the second puzzle
Skip the story dialogues 20 times
Clicked the next puzzle button in the first stage
Complete a puzzle without using the hint button
Complete the first puzzle
Turn off the In-Game Music
Skip the Introduction story