Like "No Diving", this achievement seems to be extremely glitchy. After a couple of hours of trying, I unlocked this on a completely random run that I was sure I failed. I did clip it, though, so you can see it here:
This confirms a few of the mechanics of the achievement, at least:
- You just need to get from one keystone to the next without touching the floor.
- Touching the wall (even grassy wall) is fine.
- I'm guessing you also can't touch the floor for a few seconds after picking up the green keystone. This is very annoying, as Doodle will drop your tail once you do. As you can see, my tail drops at the end, but only after a few seconds.
- The achievement unlocked for me a second after the green keystone appeared in its outline.
- I had a very poor jump in this clip. You can actually jump directly to the green keystone (though I haven't managed to do this without my tail dropping to the ground).
- I started the level fresh from the level select menu (NOT using retry). No idea if this is necessary, but doing this is what got me No Diving, so who knows?
All I can suggest is that this achievement's requirements are bugged and enough attempts will randomly get it for you.
EDIT: As of June 21, 2017, this has reportedly been patched. I'll leave the solution up, but hopefully this is much more doable now.