Aims. We study the chromosphere and corona of the ultra-fast rotator AB Dor A at high temporal and spectral resolution using simultaneous observations with XMM-Newton in the X-rays, VLT/UVES in the optical, and the ATCA in the radio. Our optical spectra have a resolving power of ∼50 000 with a time cadence of ∼1 min. Our observations continuously cover more than one rotational period and include both quiescent periods and three flaring events of different strengths. Methods. From the X-ray observations we investigated the variations in coronal temperature, emission measure, densities, and abundance. We interpreted our data in terms of a loop model. From the optical data we characterised the flaring chromospheric material using numerous emission lines that appear in the course of the flares. A detailed analysis of the line shapes and line centres allowed us to infer physical characteristics of the flaring chromosphere and to coarsely localise the flare event on the star. Results. We specifically used the optical high-cadence spectra to demonstrate that both turbulent and Stark broadening are present during the first ten minutes of the first flare. Also, in the first few minutes of this flare, we find short-lived (one to several minutes) emission subcomponents in the Hα and Ca ii K lines, which we interpret as flare-connected shocks owing to their high intrinsic velocities. Combining the space-based data with the results of our optical spectroscopy, we derive flare-filling factors. Finally, comparing X-ray, optical broadband, and line emission, we find a correlation for two of the three flaring events, while there is no clear correlation for one event. Also, we do not find any correlation of the radio data to any other observed data.