This Letter presents a search for direct production of charginos and neutralinos via electroweak interactions. The results are based on data from proton-proton collisions at a center-of-mass energy of 13 TeV collected with the CMS detector at the LHC, corresponding to an integrated luminosity of 137 fb^-1. The search considers final states with large missing transverse momentum and pairs of hadronically decaying bosons WW, WZ, and WH, where H is the Higgs boson. These bosons are identified using novel algorithms. No significant excess of events is observed relative to the expectations from the standard model. Limits at the 95% confidence level are placed on the cross section for production of mass-degenerate wino-like supersymmetric particles χ˜₁^± and χ˜₂⁰, and mass-degenerate higgsino-like supersymmetric particles χ˜₁^±, χ˜₂⁰, and χ˜₃⁰. In the limit of a nearly-massless lightest supersymmetric particle χ˜₁⁰, wino-like particles with masses up to 870 and 960 GeV are excluded in the cases of χ˜₂⁰ → Zχ˜₁⁰ and χ˜₂⁰ → Hχ˜₁⁰, respectively, and higgsino-like particles are excluded between 300 and 650 GeV.