Here is the full list of all 32 Star Hunter DX achievements.
Unlock CAT-99
Clear Stage 2
Collect a 1-UP item
Start a game in Bullet Hell mode
Rescue all 30 astronauts
Clear Stage 1
Recharge a bomb
Use bullet time
Collect a high value energy cube
Read the How to Play guide
Clear Stage 3
Clear Stage 4
Clear Stage 5
Clear Stage 6
Clear Bounty Hunter mode without continuing
Clear any mode without continuing or using bullet time
Clear Bullet Hell mode without continuing
Clear the game with CAT-99
Clear the game with Luna
Clear the game with Edgar
Continue on Stage 1
Clear Stage 5 without dying
Play any stage in Practice mode
Unlock Edgar
Rescue all astronauts in Stage 4
Rescue 15 astronauts
Only collect gold at x8 multiplier on any stage
Don't kill any jellyfish in Stage 3
Trigger a boss escape pod
Destroy the Stage 5 boss' escape pod
Defeat the Stage 1 boss with 50 seconds remaining
Score over 30,000,000 points