We describe a recently realized experiment producing the most spherical cavitation bubbles today. The bubbles grow inside a liquid from a point plasma generated by a nanosecond laser pulse. Unlike in previous studies, the laser is focussed by a parabolic mirror, resulting in a plasma of unprecedented symmetry. The ensuing bubbles are sufficiently spherical that the hydrostatic pressure gradient caused by gravity becomes the dominant source of asymmetry in the collapse and rebound of the cavitation bubbles. To avoid this natural source of asymmetry, the whole experiment is therefore performed in microgravity conditions (ESA, 53rd and 56th parabolic flight campaign). Cavitation bubbles were observed in microgravity (∼0 g), where their collapse and rebound remain spherical, and in normal gravity (1 g) to hyper-gravity (1.8 g), where a gravity-driven jet appears. Here, we describe the experimental setup and technical results, and overview the science data. A selection of high-quality shadowgraphy movies and time-resolved pressure data is published online.