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