  We study a class of realizations of the Next-to-Minimal Supersymmetric
Standard Model that is motivated by dark matter and Higgs data, and in which
the lightest pseudoscalar Higgs boson mass is smaller than twice the bottom
quark mass and greater than twice the tau lepton mass. In such scenarios, the
lightest pseudoscalar Higgs boson can be copiously produced at the LHC from the
decay of heavier superpartners and will dominantly further decay into a pair of
tau leptons that is generally boosted. We make use of a boosted object tagging
technique designed to tag such a ditau jet, and estimate the sensitivity of the
LHC to the considered supersymmetric scenarios with 20 to 50~fb$^{-1}$ of
proton-proton collisions at a center-of-mass energy of 13~TeV.
