I've given up on the 2nd boss, and a walkthrough I found didn't convince me there's a good way to beat it. While the 1st is good, with predictable patterns and all its body free to attack, the 2nd needs you to hit its head. The problem is you need to jump on the gun it uses, then get one shot before it punches you off. It'll be fast to do so, and that stuns you to probably lose a life by a laser shot. You can potentially get a few shots with jumping away, then turning to fire, but that's fairly technical especially with an uncertain landing.
Then again, the real game is on consoles, and that looks pretty good. This one is decent and simple enough, but I would've liked maybe a diagonal shot here to make Boss 2 more bearable. Just my personal take on one of Newgrounds's mascots.