Several extensions of the Standard Model predict the production of dark matter particles at the LHC. An uncharted signature of dark matter particles produced in association with VV = (WW -/+)-W-+/- or ZZ pairs from a decay of a dark Higgs boson s is searched for using 139 fb(-1) of pp collisions recorded by the ATLAS detector at a center-of-mass energy of 13 TeV. The s -> V(q (q) over bar )V(q (q) over bar) decays are reconstructed with a novel technique aimed at resolving the dense topology from boosted VV pairs using jets in the calorimeter and tracking information. Dark Higgs scenarios with m(s) > 160 GeV are excluded.