The recent discovery by Cantalupo et al. (2014) of the largest (~500 kpc) and luminous Ly-alpha nebula associated with the quasar UM287 (z=2.279) poses a great challenge to our current understanding of the astrophysics of the halos hosting massive z~2 galaxies. Either an enormous reservoir of cool gas is required $Msimeq10^{12}$ $M_{odot}$, exceeding the expected baryonic mass available, or one must invoke extreme gas clumping factors not present in high-resolution cosmological simulations. However, observations of Ly-alpha emission alone cannot distinguish between these two scenarios. We have obtained the deepest ever spectroscopic integrations in the HeII and CIV lines with the goal of detecting extended line emission, but detect neither line to a 3$sigma$ limiting SB $simeq10^{-18}$ erg/s/cm$^2$/arcsec$^2$. We construct models of the expected emission spectrum in the highly probable scenario that the nebula is powered by photoionization from the central hyper-luminous quasar. The non-detection of HeII implies that the nebular emission arises from a mass $M_{rm c}lesssim6.4times10^{10}$ $M_{odot}$ of cool gas on ~200 kpc scales, distributed in a population of remarkably dense ($n_{rm H}gtrsim3$ cm$^{-3}$) and compact ($Rlesssim20$ pc) clouds, which would clearly be unresolved by current cosmological simulations. Given the large gas motions suggested by the Ly-alpha line ($vsimeq$ 500 km/s), it is unclear how these clouds survive without being disrupted by hydrodynamic instabilities. Our study serves as a benchmark for future deep integrations with current and planned wide-field IFU such as MUSE, KCWI, and KMOS. Our work suggest that a $simeq$ 10 hr exposure would likely detect ~10 rest-frame UV/optical emission lines, opening up the possibility of conducting detailed photoionization modeling to infer the physical state of gas in the CGM.