We report the detection of O vi λλ1031, 1037 and N v λλ1238, 1242 absorption in a system of ‘mini-broad’ absorption lines (mini-BALs) previously reported to have variable C iv λλ1548, 1550 in the quasar PG0935+417. The formation of these lines in an extremely high velocity outflow (with v∼−50 000 km s−1) is confirmed by the line variability, broad smooth absorption profiles and partial covering of the background light source. H i and lower-ionization metals are not clearly present. The line profiles are complex and asymmetric, with full widths at half-minimum (FWHM) of different components in the range ∼660 to ∼2510 km s−1. The resolved O vi doublet indicates that these lines are moderately saturated, with the absorber covering ∼80 per cent of the quasar continuum source (Cf∼ 0.8). We derive ionic column densities of the order of 1015 cm−2 in C iv and several times larger in O vi, indicating an ionization parameter of log U≳−0.5. Assuming solar abundances, we estimate a total column density of NH∼ 5 × 1019 cm−2. Comparisons to data in the literature show that this outflow emerged sometime between 1982 when it was clearly not present and 1993 when it was first detected. Our examination of the C iv data from 1993 to 2007 shows that there is variable complex absorption across a range of velocities from −45 000 to −54 000 km s−1. There is no clear evidence for acceleration or deceleration of the outflow gas. The observed line variations are consistent with either changes in the ionization state of the gas or clouds crossing our lines of sight to the continuum source. In the former case, the recombination times constrain the location of outflow to be at a radial distance of r≲ 1.2 kpc with density of nH≳ 1.1 × 104 cm−3. In the latter case, the nominal transit times of moving clouds indicate r≲ 0.9 pc. Outflows are common in active galactic nuclei (AGN), but extreme speeds such as those reported here are extremely rare. It is not clear what properties of PG 0935+417 might produce this unusual outflow. The quasar is exceptionally luminous, with L∼ 6 × 1047 erg s−1, but it has just a modest Eddington ratio, L/LEdd∼ 0.2, and no apparent unusual properties compared to other quasars. In fact, PG 0935+417 has significantly less X-ray absorption than typical BAL quasars even though its outflow has a degree of ionization typical of BALs at speeds that are 2–3 times larger than most BALs. These results present a challenge to theoretical models that invoke strong radiative shielding in the X-rays/far-UV to moderate the outflow ionization and thus enable its radiative acceleration to high speeds.