  Search for compressed supersymmetry at multi-TeV scale, in the presence of a
light gravitino dark matter, can get sizable uplift while looking into the
associated fat-jets with missing transverse momenta as a signature of the boson
produced in the decay process of much heavier next-to-lightest sparticle. We
focus on the hadronic decay of the ensuing Higgs and/or $Z$ boson giving rise
to at least two fat-jets and $\slashed{E}_T$ in the final state. We perform a
detailed background study adopting a multivariate analysis using a boosted
decision tree to provide a robust investigation to explore the discovery
potential for such signal at 14 TeV LHC considering different benchmark points
satisfying all the theoretical and experimental constraints. This channel
provides the best discovery prospects with most of the benchmarks discoverable
within an integrated luminosity of $\mathcal{L}=200$ fb$^{-1}$. Kinematic
observables are investigated in order to distinguish between compressed and
uncompressed spectra having similar event yields.
