Here is the full list of all 41 Astebreed trophies - there are 24 bronze, 13 silver, 3 gold and 1 platinum.
Used Blade to destroy 20,000 enemies and their attacks.
Avoided all of the Lucis capture attacks in Chapter 5.
Used Shot to destroy 20,000 enemies and their attacks.
Earned 500,000 pts by using an EX Attack.
Cleared the game on the Easy Difficulty without using continues. (Chapter Select is not allowed.)
All demo scenes have been skipped.
Reached a total score of 100,000,000pts.
Destroyed 100 enemies and their attacks using a Spin EX Attack.
Continued 5 times.
Cleared the game on the Easy Difficulty.
Destroyed a boss using an EX Attack.
Used the Wild EX Attack 10 times.
Destroyed Asymptote Void and all its parts in Chapter 5.
Used an EX Attack to knock a direct attack from Asymptote Void back in Chapter 5.
Used the Blade to knock a direct attack from Asymptote Void back in Chapter 5.
Reached a total Lock Level of 15,000.
Destroyed Dux's outer shell in Chapter 4 by attacking mostly from the outside.
Destroyed 30 of Dux's batteries in Chapter 4.
Saw every attack pattern used by Asymptote Esto in Chapter 3.
Destroyed the entire enemy fleet in Chapter 3.
Locked onto 50 targets at the same time.
Used a Blade Dash attack to get a x16 multiplier ten times in total.
Destroyed Asymptote Esto in Chapter 2 swiftly.
Cleared a chapter on the Easy Difficulty without taking damage.
Destroyed Agnesi in Chapter 1 but kept its arms intact.
All the Tutorials have been viewed.
Played the Prologue to the end.
Get all trophies.
Cleared the game on the Easy Difficulty with less than 50,000 damage taken in total. (Chapter Select is not allowed.)
Cleared a chapter on the Normal Difficulty without taking damage.
Cleared the game on the Normal Difficulty.
Cleared the game on the Normal Difficulty without using continues. (Chapter Select is not allowed.)
Cleared the game on the Normal Difficulty with less than 50,000 damage taken in total. (Chapter Select is not allowed.)
Cleared a chapter on the Hard Difficulty without taking damage.
Cleared the game on the Hard Difficulty.
Cleared the game on the Hard Difficulty without using continues. (Chapter Select is not allowed.)
Cleared the game on the Hard Difficulty with less than 50,000 damage taken in total. (Chapter Select is not allowed.)
Cleared the game with all mecha on all Difficulties.
Reached a total score of 300,000,000pts.
Used a Dash EX attack to get a x16 multiplier 30 times in total.
Destroyed Queen System in Chapter 6 without taking any damage.