Knock the first boss down. Now close in on him and crouch, then spam Punch+Kick together for a bit. You'll hear a jackhammering noise and see him go down in about a couple of seconds. LOL, that was so easy. This could be used to help your time bonus, or allow you to back up and do a little more point-pressing. It will only work on this boss.
One caveat: This won't work on the PCENGINE/TurboGrafx-16 version if you have the nunchucks. So you'll either have to not pick them up for the first stage, or take one hit as you're getting closer to the boss.
The same trick can be used on the arcade/PS4/Xbox One version even if you're carrying nunchucks, but not at all on the Sega Mark III (Master System).
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