This trophy is part of A Star Is Born, Rising Star and Mega Star trophies; essentially, you'll need to achieve 5/5 stars on all ten chapters to complete these together. At the end of a completed chapter, you'll see what you received for that run and see what your best run was; likewise, on chapter select, you'll see your best rated run.
While I don't believe it explicitly states what is required for ratings, how well you perform is correlated. Stats people infer that define the star rating are: damage taken, how many times you die or fail a puzzle, accuracy with weapon, accuracy with stasis, and items collected, specifically audio and text logs, weapons, and weapon upgrades
. You will see all your stats at the end of each chapter to see where you might have had issues or glean some improvements. Of course, each stat relates, so if you died a lot, it's likely you took lots of damage and had worse accuracy. Not sure if difficulty plays a role in calculating your star rating for each chapter, but it stands to reason that on Easy, one will take less damage and enemies will die more easily making it more likely to have a better rating.