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