In order to obtain all achievements, the game most be won 3 times. There are two additional modes as well with their own achievements: Boss rush (endless) and Hardcore.
Note that all can be unlocked in easy difficulty and I suggest playing on that if you find the game overwhelmingly difficult.

The basic layout for a game is 3 Levels followed by a final boss level. Each level consists of various enemies, a chance for a mad event, and a boss fight.

It’s also worth mentioning that the hit box is the small circle on your ship. No wing damage!

• Movement: Arrow keys
  
• Fire: z
  
• Slow down: shift
  
• Use picked up item: space

I found using a gamepad worked great and rebound the keys using AntiMicro[github.com]. That way I could also toggle the fire and slow down on and off. The slow down ability is great for dodging in boss fights and when large quantities of bullets flood the screen. Note that it also impairs the ship’s movement somewhat and cannot move at all when being pulled in by some enemies.

These are not tied to any particular game

Play through the entire game the first time to unlock these

During the second play through of the game these will unlock

Play through the game a third time for these

These achievements are unlocked in either the Boss Rush (endless) or hardcore special modes:

Divinity Slayer Video:
https://www.youtube.com/watch?v=TakAVyIv_W4
Lunatic! Video:
https://www.youtube.com/watch?v=9B1nh7EE6FA