Beaver boss unkillable?

[Life is meaningless]

I've tried killing the bever boss forever and i've yet to succeed even having runs lasting well over 15 min of just constant shooting.

[A. Moreira]

Just went past this boss.
In the brief moment that his stomach is invulnerable, he will start concentrating, and shoot that fiery beam from his eyes.
You have to get real close, point your gun at this head and fire your beam continuously (if you do it from too far away, you will get burned).
If you succeed, the scenery will change (more hazards will appear), and the boss pattern will repeat. You have to do it once again in the end.