Mistake on my part, I believe NG+ is not required.
Hscene for chapter 3:
Your main goal is for Ayumu to gain skill Independent Heart and use it at least once in the final battle with the shrine maidens.
Hscene for Chapter 2:
Obtain skill Sister Blade and use it on final battle of that chapter.
Hscene for Chapter 4:
Gain Absolute Horizon and use on final battle of Chapter 4.
In short, try to meet the requirements/events in order for Ayumu to gain special skill on each chapter and use it at the main battle.