I tested it a few times now and I can't get the Bossfight skip... I managed to skip the cutscene before the fight nearly everytime, but for some reason even if i mimic the strats which others on the leaderboard did. I can't damage Anakin after that.

I recommend continuing to watch the videos on the leaderboard and continue to try. Sometimes it works for me and sometimes not. I don't know exactly what determines if it works or not, but I try to stay as far as possible on the edge on the ground, and when I jump out towards the lava, I try to jump as short out from the ground, but as far to the right as I can, so after the two double jumps you have come as far to the other side as possible. If you are successful, you will see some glitched hearts on your screen when you are hitting Darth Vader. Me doing it: Not the best quality, but it shouldn't be a problem to see. Time in video: 6:45