Here is the full list of all 10 Thundering Skies achievements.
Defeat The Master.
Beat the game in Beginner without dying.
Get an extra ship by picking a power-up with all weapons already maxed out.
Get killed by both overheating and freezing in the same playthrough.
Beat the game in Easy, Normal or Hard with a single credit.
Get a S Rank in Normal or Hard.
Use a cheat code.
Beat the game in Easy, Normal or Hard in Arcade Mode.
Complete any stage in Easy, Normal or Hard firing only Level 1 Straight or Rear Shots.
Get from Jupiturn's top clouds to core without dying.