This Seeking Tech guide will explain how you can easily beat the Danger Dojo Dragon in Astro Bot. Use the following video as a reference:
The enemy will first appear on the top area of the screen.
Afterwards, the weak spots will be more towards the middle of the screen. This is the easiest time to hit the pink spots, so make sure you rapidly throw your shuriken. It will then move to the top and then slant down to the middle again.
If you are accurate, then you should be close to beating the dragon. Take out any spirits he shoots at you and then destroy the remaining weak spots to end the fight.