BOSS-EUVLG1 is the most ultraviolet (UV) and Lyα luminous galaxy to be going through a very active starburst phase detected thus far in the Universe. It is forming stars at a rate of 955 ± 118 M⊙ yr‒1. We report the detection of a broad Hα component carrying 25% of the total Hα flux. The broad Hα line traces a fast and massive ionized gas outflow characterized by a total mass, log(Mout[M⊙]), of 7.94 ± 0.15, along with an outflowing velocity (Vout) of 573 ± 151 km s‒1 and an outflowing mass rate (Ṁout) of 44 ± 20 M⊙ yr‒1. The presence of the outflow in BOSS-EUVLG1 is also supported by the identification of blueshifted UV absorption lines in low and high ionization states. The energy involved in the Hα outflow can be explained by the ongoing star formation, without the need for an active galactic nucleus to be included in the scenario. The derived low mass-loading factor (η = 0.05 ± 0.03) indicates that, although it is massive, this phase of the outflow cannot be relevant for the quenching of the star formation, namely, the negative feedback. In addition, only a small fraction (≤15%) of the ionized outflowing material with velocities above 372 km s‒1 has the capacity to escape the gravitational potential and to enrich the surrounding circumgalactic medium at distances above several tens of kpc. The ionized phase of the outflow does not carry sufficient mass or energy to play a relevant role in the evolution of the host galaxy nor in the enrichment of the intergalactic medium. As predicted by some recent simulations, other phases of the outflow could be responsible for most of the outflow energy and mass in the form of hot X-ray emitting gas. The expected emission of the extended X-ray emitting halo associated with the outflow in BOSS-EUVLG1 and similar galaxies could be detected with the future ATHENA X-ray observatory, however, there are no methods at present that would assist in their spatial resolution.