This trophy is part of A Star Is Born, Super 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.
*** Spoiler - click to reveal ***
That said, I think what really affected the rating most was how many main collectibles you acquired. After playing through a chapter, if you collected any of the weapon upgrades, on repeat playthroughs, those won't appear in the level but the other collectibles will, meaning you should try to collect all the collectibles again when trying to 5 star a level. For collectibles, use Lukey52's guide here: https://www.playstationtrophies.org/forum/dead-space-extract...
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It might be overkill to include this but I kept track of my stats to see the difference between the star ratings for myself; and to include them now to see how yours line up. Not sure if it'll be of any help, but it might. I denoted on Chapters 2, 6, 9 that I got four stars on the Hard playthrough and replayed on Impossible to get five stars--with fully upgraded gear and weapons. The other seven chapters I achieved five stars on Hard playthrough. On Chapters 3 and 10, I missed a collectible; for third level, it mattered for another trophy, and for tenth level, it didn't--but both do affect the star rating, so even with missing one I still achieved five stars rating on those levels on Hard. Here were my stats for posterity:
Mega Star stats:
Ch. 1: Worlds Apart
:+:Performance:+:
Deaths - 0
Grabs - 3
Damage Taken - 187%
Med Packs Used - 4
Revival Packs Used - 0
Puzzle Failures - 0
:+:Weapons:+:
Shots Fired - 94
Enemies Killed - 27
Perfect Reloads - 24/27
Accuracy - 80%
Dismemberments - 48
Stasis Accuracy - 89%
:+:Collectibles:+:
Items Collected - 33
Audio Logs - 1/1
Text Logs - 3/3
Weapons - 1/1
Weapon Upgrades - 2/2
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(1st - 4 stars on Hard; 2nd - 5 stars on Impossible)
Ch. 2: Another Day at the Office
:+:Performance:+:
Deaths - 1; 0
Grabs - 7; 0
Damage Taken - 171%; 44%
Med Packs Used - 4; 1
Revival Packs Used - 0
Puzzle Failures - 0
:+:Weapons:+:
Shots Fired - 120; 167
Enemies Killed - 58; 60
Perfect Reloads - 37/47; 46/47
Accuracy - 81%; 87%
Dismemberments - 44; 212
Stasis Accuracy - 77%; 93%
:+:Collectibles:+:
Items Collected - 54; 46
Audio Logs - 0/0; 0/0
Text Logs - 3/3; 3/3
Weapons - 2/2; 2/2
Weapon Upgrades - 3/3; 0/0
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(*missed out on a plasma cutter weapon)
Ch. 3: Return to the Megavents
:+:Performance:+:
Deaths - 0
Grabs - 0
Damage Taken - 140%
Med Packs Used - 4
Revival Packs Used - 0
Puzzle Failures - 3
:+:Weapons:+:
Shots Fired - 377
Enemies Killed - 63
Perfect Reloads - 49/61
Accuracy - 78%
Dismemberments - 148
Stasis Accuracy - 87%
:+:Collectibles:+:
Items Collected - 46
Audio Logs - 1/1
Text Logs - 3/3
Weapons - 2/3*
Weapon Upgrades - 4/4
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Ch. 4: Rendezvous with Fate
:+:Performance:+:
Deaths - 0
Grabs - 1
Damage Taken - 172%
Med Packs Used - 12
Revival Packs Used - 0
Puzzle Failures - 1
:+:Weapons:+:
Shots Fired - 372
Enemies Killed - 65
Perfect Reloads - 43/53
Accuracy - 75%
Dismemberments - 165
Stasis Accuracy - 77%
:+:Collectibles:+:
Items Collected - 82
Audio Logs - 1/1
Text Logs - 3/3
Weapons - 4/4
Weapon Upgrades - 4/4
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Ch. 5: Emergency Care
:+:Performance:+:
Deaths - 1
Grabs - 15
Damage Taken - 126%
Med Packs Used - 6
Revival Packs Used - 0
Puzzle Failures - 0
:+:Weapons:+:
Shots Fired - 218
Enemies Killed - 47
Perfect Reloads - 38/43
Accuracy - 74%
Dismemberments - 119
Stasis Accuracy - 80%
:+:Collectibles:+:
Items Collected - 58
Audio Logs - 1/1
Text Logs - 3/3
Weapons - 4/4
Weapon Upgrades - 5/5
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(1st - 4 stars on Hard; 2nd - 5 stars on Impossible)
Ch. 6: Nowhere to Hide
:+:Performance:+:
Deaths - 0; 0
Grabs - 4; 1
Damage Taken - 212%; 118%
Med Packs Used - 12; 6
Revival Packs Used - 0; 0
Puzzle Failures - 0; 0
:+:Weapons:+:
Shots Fired - 476; 557
Enemies Killed - 42; 45
Perfect Reloads - 57/70; 58/64
Accuracy - 65%; 67%
Dismemberments - 73; 94
Stasis Accuracy - 79%; 85%
:+:Collectibles:+:
Items Collected - 48; 37
Audio Logs - 1/1; 1/1
Text Logs - 3/3; 3/3
Weapons - 5/5; 5/5
Weapon Upgrades - 5/5; 0/0
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Ch. 7: Life and Death
:+:Performance:+:
Deaths - 0
Grabs - 5
Damage Taken - 152%
Med Packs Used - 8
Revival Packs Used - 0
Puzzle Failures - 0
:+:Weapons:+:
Shots Fired - 433
Enemies Killed - 60
Perfect Reloads - 57/62
Accuracy - 79%
Dismemberments - 136
Stasis Accuracy - 98%
:+:Collectibles:+:
Items Collected - 37
Audio Logs - 1/1
Text Logs - 3/3
Weapons - 4/4
Weapon Upgrades - 5/5
-----
Ch. 8: In the Hearts of Men
:+:Performance:+:
Deaths - 0
Grabs - 0
Damage Taken - 38%
Med Packs Used - 1
Revival Packs Used - 0
Puzzle Failures - 0
:+:Weapons:+:
Shots Fired - 203
Enemies Killed - 46
Perfect Reloads - 39/44
Accuracy - 88%
Dismemberments - 103
Stasis Accuracy - 87%
:+:Collectibles:+:
Items Collected - 21
Audio Logs - 1/1
Text Logs - 2/2
Weapons - 5/5
Weapon Upgrades - 4/4
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(1st - 4 stars on Hard; 2nd - 5 stars on Impossible)
Ch. 9: Escaping the Ishimura
:+:Performance:+:
Deaths - 1; 0
Grabs - 18; 17
Damage Taken - 361%; 222%
Med Packs Used - 12; 16
Revival Packs Used - 1; 0
Puzzle Failures - 0; 0
:+:Weapons:+:
Shots Fired - 1406; 1248
Enemies Killed - 119; 122
Perfect Reloads - 88/103; 96/96
Accuracy - 44%; 59%
Dismemberments - 158; 163
Stasis Accuracy - 71%; 84%
:+:Collectibles:+:
Items Collected - 112; 104
Audio Logs - 1/1; 1/1
Text Logs - 3/3; 3/3
Weapons - 8/8; 8/8
Weapon Upgrades - 5/5; 0/0
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(*missed the audio log)
Ch. 10: Secrets and Salvation
:+:Performance:+:
Deaths - 0
Grabs - 10
Damage Taken - 89%
Med Packs Used - 4
Revival Packs Used - 0
Puzzle Failures - 0
:+:Weapons:+:
Shots Fired - 343
Enemies Killed - 64
Perfect Reloads - 63/70
Accuracy - 77%
Dismemberments - 138
Stasis Accuracy - 92%
:+:Collectibles:+:
Items Collected - 16
Audio Logs - 0/1*
Text Logs - 1/1
Weapons - 1/1
Weapon Upgrades - 3/3