Here is the full list of all 39 Ginga Force trophies - there are 18 bronze, 17 silver, 3 gold and 1 platinum.
Chapter X cleared in story mode
Played all of the chapters in story mode.
Selected designated equipment (Heavy Laser Gun, Homing Missile, Counter Shield).
Clear story mode on EASY.
Chapter 10 cleared in story mode
Chapter 9 cleared in story mode
Narrowly escaped a game over by getting an Extend Item.
Chapter 8 cleared in story mode
Chapter 7 cleared in story mode
Clear after destroying two elevator shafts in Chapter 7. (Story mode only)
Destroyed an enemy ship using backfire while changing speeds!
Clear after completely exposing the boss with the search lights in Chapter 2. (Story mode only)
Uploaded your score to the Online Rankings.
Chapter 6 cleared in story mode
Clear while successfully protecting the shuttle in Chapter 6. (Story mode only)
Chapter 5 cleared in story mode
Chapter 4 cleared in story mode
Chapter 3 cleared in story mode
Clear after shooting down both missiles in Chapter 3. (Story mode only)
Chapter 2 cleared in story mode
Chapter 1 cleared in story mode
Clear at highest “Target Parts Destroyed” rank in Chapter 1. (Story mode only)
Obtained all trophies
Chapter Y cleared in story mode
Clear story mode on NORMAL.
Clear story mode on HARD.
Clear at highest “Target Parts Destroyed” rank in Chapter 4. (Story mode only)
Clear at highest “Septonium Collection” rank in Chapter 5. (Story mode only)
Clear at highest rank for enemy ships shot down in the second half in Chapter 8. (Story mode only)
Clear at highest “Target Parts Destroyed” rank in Chapter 9. (Story mode only)
Played all of the chapters in score attack.
Clear Chapter 9 using the center→left→right route order. (Story mode only)
Increased initial lives to the maximum 30 ships in any chapter. (Story mode only)
Got shaken off by the suspect in the very first battle in Chapter 1! (Story mode only)
Cleared Chapter 2 without using the Jamming Unit while avoiding detection by the search lights. (Story mode only)
Total score surpassed 500,000,000 points. (Story mode only)
Cleared all chapters of story mode in any difficulty in under 1 hour total. (Story mode only, including Special Chapters)
Reach a total of 1,000,000 credits. (Story mode only)
Watch a rival’s replay. (The same chapter in Score Attack must be played.)