We study the decay \(\bar{B}^{0}\rightarrow\Lambda_{c}^{+}\bar{p}\pi^{+}\pi^{-}\), reconstructing the \Lambda_{c}^{+} baryon in the \(p K^{-}\pi^{+}\) mode, using a data sample of \(467\times 10^{6}\) \(B\bar{B}\) pairs collected with the BaBar detector at the PEP-2 storage rings at SLAC. We measure branching fractions for decays with intermediate \(\Sigma_{c}\) baryons to be \({\cal B}\bar{B}^{0}\rightarrow\Sigma_{c}(2455)^{++}\bar{p}\pi^{-}=(21.3 \pm 1.0 \pm 1.0 \pm 5.5) \times 10^{-5}\), \({\cal B}\bar{B}^{0}\rightarrow\Sigma_{c}(2520)^{++}\bar{p}\pi^{-}=(11.5\pm 1.0 \pm 0.5 \pm 3.0)\times 10^{-5}\), \({\cal B}\bar{B}^{0}\rightarrow\Sigma_{c}(2455)^{0}\bar{p}\pi^{+}=(9.1 \pm 0.7 \pm 0.4 \pm 2.4)\times10^{-5}\), and \({\cal B}\bar{B}^{0}\rightarrow\Sigma_{c}(2520)^{0}\bar{p}\pi^{+}= (2.2 \pm 0.7 \pm 0.1\pm 0.6) \times 10^{-5}\), where the uncertainties are statistical, systematic, and due to the uncertainty on the \(\Lambda_{c}^{+}\rightarrow\proton\Km\pi^{+}\) branching fraction, respectively. For decays without \(\Sigma_{c}(2455)\) or \(\Sigma_{c}(2520)\) resonances, we measure \({\cal B}\bar{B}^{0}\rightarrow\Lambda_{c}^{+}\bar{p}\pi^{+}\pi^{-}_{\mathrm{non-\Sigma_{c}}}=(79 \pm 4 \pm 4 \pm 20)\times10^{-5}\). The total branching fraction is determined to be \({\cal B}\bar{B}^{0}\rightarrow\Lambda_{c}^{+}\bar{p}\pi^{+}\pi^{-}_{\mathrm{total}}=(123 \pm 5 \pm 7 \pm 32)\times10^{-5}\). We examine multibody mass combinations in the resonant three-particle \(\Sigma_{c}\bar{p}\pi\) final states and in the four-particle \(\Lambda_{c}^{+}\bar{p}\pi^{+}\pi^{-}\) final state, and observe different characteristics for the \(\bar{p}\pi\) combination in neutral versus doubly-charged \(\Sigma_{c}\) decays.