Context. In recent years, Lyα nebulae have been routinely detected around high redshift, radio-quiet quasars thanks to the advent of the highly sensitive integral field spectrographs. Constraining the physical properties of the Lyα nebulae is crucial for a full understanding of the circum-galactic medium (CGM). The CGM acts both as a repository for intergalactic and galactic baryons as well as a venue of feeding and feedback processes. The most luminous quasars are privileged test-beds to study these processes, given their large ionising fluxes and dense CGM environments in which they are expected to be embedded. Aims. We aim to characterise the rest-frame ultraviolet (UV) emission lines in the CGM around a hyper-luminous, broad emission line, radio-quiet quasar at z ∼ 3.6, which exhibits powerful outflows at both nuclear and host galaxy scales. Methods. We analyse VLT/MUSE observations of the quasar J1538+08 (L_bol = 6 × 10⁴⁷ erg s⁻¹), and we performed a search for extended UV emission lines to characterise its morphology, emissivity, kinematics, and metal content. Results. We report the discovery of a very luminous (∼2 × 10⁴⁴ erg s⁻¹), giant Lyα nebula and a likely associated extended (75 kpc) CIV nebula. The Lyα nebula emission exhibits moderate blueshift (∼440 km s⁻¹) compared to the quasar systemic redshift and a large average velocity dispersion (σ¯_v ∼ 700 km s⁻¹) across the nebula, while the CIV nebula shows average velocity dispersion of σ¯_v ∼ 350 km s⁻¹. The Lyα line profile exhibits a significant asymmetry towards negative velocity values at 20−30 kpc south of the quasar and is well parametrised by the following two Gaussian components: a narrow (σ ∼ 470 km s⁻¹) systemic one plus a broad (σ ∼ 1200 km s⁻¹), blueshifted (∼1500 km s⁻¹) one. Conclusions. Our analysis of the MUSE observation of J1538+08 reveals metal-enriched CGM around this hyper-luminous quasar. Furthermore, our detection of blueshifted emission in the emission profile of the Lyα nebula suggests that powerful nuclear outflows can propagate through the CGM over tens of kiloparsecs.