Base Game (Default Music) - Play Iyaiya on Hard (4) and jump over the enemies. It doesn't matter if a enemy hits you, as long as you reach the end without hitting any enemies.
Just as Planned Plus - Play any Touhou Project collab song with it set to the dodge mode. You can do this by going to Hakurei Reimu in the character select and double clicking her yin-yangs. This changes all Touhou songs to Touhou styled dodge maps. Since there are no enemies, you'll get this achievement upon completing any of them. You'll also get the "Inner World" achievement if you don't have it, since they are all hidden maps. Double click the yin-yangs again to go back to normal play.