As most others have said: hitboxes are a bit of a mystery and weapons need feedback. You could also remember the last input direction so neutral attacks don’t always go left. Seeing as the bosses are big give them colliders to prevent the player walking through them.
I think the web version is a bit janky (macOS, Firefox). The killer whale battle didn’t work. It loads up but then freezes: player doesn’t move, enemy doesn’t move. Couldn’t damage the jelly. A couple of times the mushroom fight froze when it spawns the little shrooms. That sweet music continues playing though. Keep that sweet music.
Nice early prototype. Looking forward to seeing it developed.