Here is the full list of all 13 Super Galaxy Squadron EX Turbo achievements.
Achieve Rank A or above in Endless Mode
Beat Boss Rush
Beat a stage on Hardcore Hell mode
Get the Max Bonus against Albatross
Find all secret medals in a stage
Get the Max Bonus against Iron Helix
Get the Max Bonus against Great Rift
Get the Max Bonus against Hell Diver
Finish with a total score of 15 million or above
Finish the game
Achieve Rank S or above in Endless Mode
Achieve Rank SS or above in Endless Mode
Beat Hardcore Arcade Mode for that time-honored 1CC