Halfmoon City is among the most difficult stages. There's a really fast enemy/robot, you need to remain in the pocket until it gets boxed-in by slower-moving robots, then dash upwards for the goal. It's still very hard even if you know what to do.
For direct walkthroughs, you can message me at rpgmaker.net(Ruihiro_Jirishima) since this site doesn't allow direct messaging.
I can answer questions regarding other difficult stages, as well.