Side Scroller: Moving Along the Y-Axis via Single Button Press

I’m attempting to walk a character from a certain distance of the Y-Axis to another point. In the code I’ve cobbled together, however, my character simply rotates slightly; there isn’t any actual Y-Axis movement. Is my character locked onto the Y-Axis, or is there some sort of other means for my character to move from one “tier” to the next?

Alternatively, if there was a way to have a character “lock” onto a portion of the floor and move to another section of the floor up the Y-axis, that’d essentially be what I’m aiming to do as well.

You can use splines to have the character walk/run on and that would be the distance it needs to walk.