There is a way to speed up the process of earning the Virtual Virgin and Enscrewsiast achievements. This was tested twice with my own and my alt account. I used an actual second account for the second controller instead of choosing "I don't care" just to be safe.
Start a game and on the first question, have your second account screw your main account with the RT button. Answer the question correctly to defeat the screw attack. Wait for the introduction to question 2 to complete (The yodeling part) before quitting out to the main menu. There is no indication that the game is saving your progress but it is, even though the game warns that all progress will be lost. This is faster than completing a whole episode since you only get one screw a game. Repeat 5 times. Achievement will unlock a few moments after the 5th successful attempt.