A truly annoying achievement. For this, you will have to beat each level while avoiding as many notes as possible, and pretty much completely without killing enemies. Most levels are fairly simple, but a few can cause problems.
For the most part, try to take it slow and use the simplest path through each level. Let flying enemies pass you by, and just avoid the stationary ones. If an enemy is blocking your path completely, don't be afraid to run into him and use the invulnerability period after getting hit to slip through. This is very useful for level 9 especially.
Level 9 and 10 are the biggest annoyances here, and that's mainly because of the cart sections. You WILL take damage from the enemies in these, but the real issue are the notes on the tracks, that you really can't avoid. But you can avoid SOME, by speeding up or slowing down in certain sections. Experiment! Level 9 is particularly bad because the level ends when you free the guy at the end, which gives you 10 points whether you want them or not. So you really only have 9 points of leeway for the rest of the level. I'm not sure if 20 is okay, just use 19 as a maximum value to make sure it counts.
Level 10 is mainly bad because of the start. You have to avoid getting on the carts to make it through here. Instead, for at least half the section, just keep falling into the pits and bouncing up again, hovering as far as you can each time. It's weird, but it's the only way to do it. There's also a troublesome big enemy in the building before the boss, I would advise you lead him all the way down and out the door on the left, so he's not in your way when you run after activating the switch.
All in all, this is not a very fun achievement, but with a little perseverance it's not the worst thing in the world either.