My continuous variable has a lot of observations on the leftmost and rightmost tails but not so many in the middle. Is there a transformation that is recommended, or should I segment the data into an ordinal/binary one?
The first question that springs to mind is do you expect this to be consistent with outliers? Of course, it depends on what your other variable is and how it was measured. I would be keen to know if you are in a position to share, the source of your data series and type of instrument (if any).
If your observations are from measurements taken using an instrument when interpreting signal processing, It's easy to fall into the trap of disregarding the dynamic response function of the instrument itself as they lose linearity at the extremes.
Signal processing of this kind will also expose you to harmonics.
What you have is a continuous series who's observation count with respect to the continuous variable can be modeled using regression. Have you attempted to fit a polynomial function to the data or does it appear like an elongated cosine function?
I am trying to picture it to give a suggestion unless you are familiar with decision tree algorithms?
I do not know why you want to transform data as the data already are in binary mode.