The Hair node should not be plugged into diffuse, it should be plugged in Alt-Diffuse. Switch off Diffuse and Specular.

As far as I know, there is no better way to shade dynamic hair.

A ship in port is safe; but that is not what ships are built for.
Sail out to sea and do new things.
-"Amazing Grace" Hopper

Avatar image of me done by Chidori.