  We propose a scheme to explore regimes of strong-field Quantum
Electrodynamics (SF-QED) otherwise unattainable with the currently available
laser technology. The scheme relies on relativistic plasma mirrors curved by
radiation pressure to boost the intensity of PetaWatt-class laser pulses by
Doppler effect and focus them to extreme field intensities. We show that very
clear SF-QED signatures could be observed by placing a secondary target where
the boosted beam is focused.
