The bug was a complete show-stopper, and I was forever stuck at the boss fight and couldn't progress. Since I wasn't writing down passwords (as absolute majority of people wouldn't, assuming the game is saving their progress... as all PC games absolutely should!) I didn't try to restart from the beginning.
I got to the boss normally - playing from level 1 until 9 dying a bunch. Not sure how the life system works, but I definitely died more than 3 times. Particularly on lv7 I must've died 5-10 times, but lives always stayed at 3. Then I proceeded to lose another two lives at the boss before defeating it. After the boss death animation, player movement control was disabled, but I could still change direction and attack. After being stuck like this for about 30 seconds the boss simply respawned and continued his attack pattern like nothing happened, eventually killing player. Once the fight restarted, I was able to defeat the boss again, but the same thing happened.