Princess does actually teleport! She gets a new attack in phase 2 that lets her do a bar-long teleport lunge at you, if you're too far away. Her AI tries to choose the best attack pattern depending on your playstyle in response. She gets a few new tools to use as the fight progresses to spice up phase 2 some. It might be getting lost in the chaos of that second phase fight though.
That dashing mechanic you suggested was also something I am considering adding - but ended up cutting for time in order to refine the initial movement in true boomer shooter fashion. Jumps initially WERE gonna be timed too, but the input just felt weird, so I ended up instead trying to make their hold time synced - so you jump whenever, but will start falling when the beat hits. It's - hit and miss, though. That FPS cap thing is an issue that came up due to last-minute moving to windows from web, meaning all my settings stuff just - broke. I forgot to put in a cap on it, and it's one of the first things I plan to do post-jam, alongside some bug fixes.
I'm glad you had fun with this! Our team was super crazy given it was me and two composers, but they absolutely cooked up a fire soundtrack that I was able to do justice. I'm super happy with how this turned out for a four-day game jam, especially given I had to hand animate stuff for all three enemy types to fit the beat on their movements.
Thank you for playing!