  The vast majority of QED results are obtained in relatively weak fields and
so in the framework of perturbation theory. However, forthcoming laser
facilities providing extremely high fields can be used to enter not-yet-studied
regimes. Here, a scheme is proposed that might be used to reach a supercritical
regime of radiation reaction or even the fully non-perturbative regime of
quantum electrodynamics. The scheme considers the collision of a 100 GeV-class
electron beam with a counterpropagating ultraintense electromagnetic pulse. To
reach these supercritical regimes, it is unavoidable to use a pulse with
ultrashort duration. Using two-dimensional particle-in-cell simulations, it is
therefore shown how one can convert a next-generation optical laser to an
ultraintense ($I\approx 2.9\times 10^{24} \text{ W} \, \text{cm}^{-2}$)
attosecond (duration $\approx$ 150 as) pulse. It is shown that if the
perturbation theory persists in extremely fields, the spectrum of secondary
particles can be found semi-analytically. In contrast, a comparison with
experimental data may allow differentiating the contribution of high-order
radiative corrections if the perturbation theory breaks.
