  Using a construction by Yamamoto of tropical contractions, we construct a
non-archimedean SYZ fibration on the Berkovich analytification of a class of
maximally degenerate hypersurfaces in projective space. We furthermore prove
that under a discrete symmetry assumption, the potential for the
non-archimedean Calabi-Yau metric is constant along the fibers of the
retraction. The proof uses the work of Li on the Fermat degeneration of
hypersurfaces, and an explicit description of toric plurisubharmonic metrics on
the hybrid space associated to a complex toric variety.
