I don't think you can avoid a 2 minute Shikieiki or Reimu fight in a no death attempt. It's 50 seconds first time without lives and 2 minutes otherwise. And there's no way you're avoiding the 5,000,000 extend.
Edit: Could be wrong and it's 2 spare lives, but that isn't likely to be avoided either.
Edit:
Ya, definitely go with Cirno. Or Tewi if you don't mind being a little cheap, but make sure to stay above 2 just in case. With Tewi, I still only got to stage 6 before dying, but it happened after the timer ran out.
Edit, yet again: Any spare lives and it's a 2 minute Shikieiki/Reimu fight. Tried again and made it to Medicine with Tewi without dying then messed up with a few seconds on the timer, then I had 2 stupid deaths on Komachi, then 2 stupid deaths on Shikieiki since the first one couldn't exactly be called stupid since it'd be hard for anyone to survive 2 minutes. Ya, I didn't even clear it that time, even though I should have.