We present a 155ks NuSTAR observation of the $z\sim 2$ hot dust-obscured galaxy (hot DOG) W1835+4355. We extracted spectra from the two NuSTAR detectors and analyzed them jointly with the archival XMM PN and MOS spectra. We performed a spectroscopic analysis based on both phenomenological and physically motivated models employing toroidal and spherical geometry for the obscurer. In all the modelings, the source exhibits a Compton-thick column density $NH\gtrsim 1024$ cm$\mathrm{<mrow\; data-mjx-texclass="ORD">-2</mrow>}$, a 2-10 keV luminosity $L2-10\approx 2\times 1045$ erg s$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$ , and a prominent soft excess ($\sim 5-10$ % of the primary radiative output), which translates into a luminosity $\sim 1044$ erg s$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$. We modeled the spectral energy distribution from 1.6 to 850 $\mu m$ using a clumpy two-phase dusty torus model plus a modified blackbody to account for emission powered by star formation in the far-infrared. We employed several geometrical configurations consistent with those applied in the X-ray analysis. In all cases we obtained a bolometric luminosity $Lbol\approx 3-5\times 1047$ erg s$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$, which confirms the hyperluminous nature of this active galactic nucleus. Finally, we estimate a prodigious star formation rate of $\sim$3000 $M\odot yr-1$, which is consistent with the rates inferred for $z\approx 2-4$ hyperluminous type I quasars. The heavily obscured nature, together with $Lbol$, the ratio of X-ray to mid-infrared luminosity, the rest-frame optical morphology, and the host star formation rate are indicative of its evolutionary stage. We can interpret this as a late-stage merger event in the transitional, dust-enshrouded, evolutionary phase eventually leading to an optically bright AGN.