  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.
