Buppousou is the boss of stage 2. Destroy it before time runs out to earn this achievement.
Tips for beginners:
The boss has two weak points; the left one is weak to dark and the right one is weak to light. When both are destroyed, the boss explodes.
First, expose the left weak point by shooting its shield with light bullets. (The right shield must be shot with dark bullets.) The shield will extend, and slowly retract when you stop shooting it. Fly in between the shield and the weak point and shoot it with dark bullets as much as you can before you have to get out again.
When Buppousou extends its arms, it is about to unleash strong attacks from alternating sides: light from the left, and dark from the right. Focus on surviving these by absorbing them, while keeping the shields open if possible. When the arms retract, fly back inside the shield and shoot the weak points some more.