A search for charginos and neutralinos at the Large Hadron Collider using fully hadronic final states and missing transverse momentum is reported. Pair-produced charginos or neutralinos are explored, each decaying into a high-pT Standard Model weak boson. Fully hadronic final states are studied to exploit the advantage of the large branching ratio, and the efficient rejection of backgrounds by identifying the high-pT bosons using large-radius jets and jet substructure information. An integrated luminosity of 139 fb(-1) of proton-proton collision data collected by the ATLAS detector at a center-of-mass energy of 13 TeV is used. No significant excess is found beyond the Standard Model expectation. Exclusion limits at the 95% confidence level are set on wino or higgsino production with various assumptions about the decay branching ratios and the type of lightest supersymmetric particle. A wino (higgsino) mass up to 1060 (900) GeV is excluded when the lightest supersymmetry particle mass is below 400 (240) GeV and the mass splitting is larger than 400 (450) GeV. The sensitivity to high-mass winos and higgsinos is significantly extended relative to previous LHC searches using other final states., ANPCyT, Argentina; YerPhI, Armenia; ARC, Australia; BMWFW, Austria; FWF, Austria; ANAS, Azerbaijan; SSTC, Belarus; CNPq, Brazil; FAPESP, Brazil; NSERC, Canada; NRC, Canada; CFI, Canada; CERN, Chile; ANID, Chile; CAS, China; MOST, China; NSFC, China; Minciencias, Colombia; MSMT CR, Czech Republic; MPO CR, Czech Republic; VSC CR, Czech Republic; DNRF, Denmark; DNSRC, Denmark; IN2P3-CNRS, France; CEA-DRF/IRFU, France; SRNSFG, Georgia; BMBF, Germany; HGF, Germany; MPG, Germany; GSRI, Greece; RGC, China; Hong Kong SAR, China; ISF, Israel; Benoziyo Center, Israel; INFN, Italy; MEXT, Japan; JSPS, Japan; CNRST, Morocco; NWO, Netherlands; RCN, Norway; MNiSW, Poland; NCN, Poland; FCT, Portugal; MNE/IFA, Romania; JINR; MES of Russia; NRC KI; Russian Federation; MESTD, Serbia; MSSR, Slovakia; ARRS, Slovenia; MIZS, Slovenia; DSI/NRF, South Africa; MICINN, Spain; SRC, Sweden; Wallenberg Foundation, Sweden; SERI, Switzerland; SNSF, Switzerland; Canton of Bern, Switzerland; Canton of Geneva, Switzerland; MOST, Taiwan; TAEK, Turkey; STFC, United Kingdom; DOE, United States of America; NSF, United States of America; BCKDF, Canada; CANARIE, Canada; Compute Canada, Canada; CRC, Canada; COST, European Union; ERC, European Union; ERDF, European Union; Horizon 2020, European Union; Marie Sklodowska-Curie Actions, European Union; Investissements d'Avenir Labex, France; Investissements d'Avenir Idex, France; ANR, France; DFG, Germany; AvH Foundation, Germany; EU-ESF, Greece; Greek NSRF, Greece; BSF-NSF, Israel; GIF, Israel; Norwegian Financial Mechanism 2014-2021, Norway; La Caixa Banking Foundation, Spain; CERCA Programme Generalitat de Catalunya, Spain; Generalitat Valenciana, Spain; Goran Gustafssons Stiftelse, Sweden; Royal Society, United Kingdom; Leverhulme Trust, United Kingdom, We thank CERN for the very successful operation of the LHC, as well as the support staff from our institutions without whom ATLAS could not be operated efficiently. We acknowledge the support of ANPCyT, Argentina; YerPhI, Armenia; ARC, Australia; BMWFW and FWF, Austria; ANAS, Azerbaijan; SSTC, Belarus; CNPq and FAPESP, Brazil; NSERC, NRC and CFI, Canada; CERN; ANID, Chile; CAS, MOSTand NSFC, China; Minciencias, Colombia; MSMT CR, MPO CR and VSC CR, Czech Republic; DNRF and DNSRC, Denmark; IN2P3-CNRS and CEA-DRF/IRFU, France; SRNSFG, Georgia; BMBF, HGF and MPG, Germany; GSRI, Greece; RGC and Hong Kong SAR, China; ISF and Benoziyo Center, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; NWO, Netherlands; RCN, Norway; MNiSW and NCN, Poland; FCT, Portugal; MNE/IFA, Romania; JINR; MES of Russia and NRC KI, Russian Federation; MESTD, Serbia; MSSR, Slovakia; ARRS and MIZS, Slovenia; DSI/NRF, South Africa; MICINN, Spain; SRC and Wallenberg Foundation, Sweden; SERI, SNSF and Cantons of Bern and Geneva, Switzerland; MOST, Taiwan; TAEK, Turkey; STFC, United Kingdom; DOE and NSF, United States of America. In addition, individual groups and members have received support from BCKDF, CANARIE, Compute Canada and CRC, Canada; COST, ERC, ERDF, Horizon 2020 and Marie Sklodowska-Curie Actions, European Union; Investissements d'Avenir Labex, Investissements d'Avenir Idex and ANR, France; DFG and AvH Foundation, Germany; Herakleitos, Thales and Aristeia programmes co-financed by EU-ESF and the Greek NSRF, Greece; BSF-NSF and GIF, Israel; Norwegian Financial Mechanism 2014-2021, Norway; La Caixa Banking Foundation, CERCA Programme Generalitat de Catalunya and PROMETEO and GenT Programmes Generalitat Valenciana, Spain; Goran Gustafssons Stiftelse, Sweden; The Royal Society and Leverhulme Trust, United Kingdom. The crucial computing support from all WLCG partners is acknowledged gratefully, in particular from CERN, the ATLAS Tier-1 facilities at TRIUMF (Canada), NDGF (Denmark, Nor