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