During the last years, Ly$alpha$ nebulae have been routinely detected around high-z, radio-quiet quasars (RQQs) thanks to the advent of sensitive integral field spectrographs. Constraining the physical properties of the Ly$alpha$ nebulae is crucial for a full understanding of the circum-galactic medium (CGM), which is a venue of feeding and feedback processes. The most luminous quasars are privileged test-beds to study these processes, given their large ionizing fluxes and dense CGM environments in which they are expected to be embedded. We aim at characterizing the rest-frame UV emission lines in the CGM around a hyper-luminous, broad emission line, RQQ at z~3.6, that exhibits powerful outflows at both nuclear and host galaxy scales. We analyze VLT/MUSE observations of the quasar J1538+08 and perform a search for extended UV emission lines to characterize its morphology, emissivity, kinematics and metal content. We report the discovery of a very luminous ($sim2 times10^{44}~erg~s^{-1}$), giant Ly$alpha$ nebula and a likely associated extended CIV nebula. The Ly$alpha$ nebula emission exhibits moderate blueshift compared with the quasar systemic redshift and large average velocity dispersion ($sigma_{v}$ ~700 $km~s^{-1}$) across the nebula, while the CIV nebula shows $sigma_{v}$~$350~km~s^{-1}$. The Ly$alpha$ line profile exhibits a significant asymmetry towards negative velocity values at 20-30 kpc south of the quasar and is well parameterized by two Gaussian components: a narrow ($sigma$~$470~km~s^{-1}$) systemic one plus a broad ($sigma$~1200 $km~s^{-1}$), blueshifted (~1500 $km~s^{-1}$) one. Our analysis of the MUSE observation of J1538+08 reveals metal-enriched CGM around this hyper-luminous quasar and our detection of blueshifted emission in the line profile of the Ly$alpha$ nebula suggests that powerful nuclear outflows can propagate through the CGM over tens of kpc.
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