You can do this on any stage, and it's really simple:
Start to dash
Immediately let go of the stick
Lightly hold in the direction you were running straight after
Basically, what happens is you are walking, but the game doesn't switch away from the running animation. When you run you can go straight off edges, while you will automatically stop to do the wobbling animation if you are walking, but, like with the walking animation, the game will keep playing the running animation instead. So in essence you start a dash, and within a split second let i go back to neutral and start walking, tricking the game into loading the wrong thing, which results in the character walking with the running animation.
Don't feel bad if it takes awhile to get the hang of it, it's lot easier in writing than it takes to actually do, I learned over a year ago and I still have trouble doing it more than 60% consistently.
