Attosecond photoelectron streaking spectroscopy allows time-resolved electron dynamics with a temporal resolution approaching the atomic unit of time. Studies have been performed in numerous systems, including atoms, molecules, and surfaces, and the quest for ever higher temporal resolution called for ever wider spectral extent of the attosecond pulses. For typical experiments relying on attosecond pulses with a duration of 200 as, the time-bandwidth limitation for a Gaussian pulse implies a minimal spectral bandwidth larger than 9 eV translating to a corresponding spread of the detected photoelectron kinetic energies. Here, by utilizing a specially tailored narrowband reflective XUV multilayer mirror, we explore experimentally the minimal spectral width compatible with attosecond time-resolved photoelectron spectroscopy while obtaining the highest possible spectral resolution. The validity of the concept is proven by recording attosecond electron streaking traces from the direct semiconductor gallium arsenide (GaAs), with a nominal bandgap of 1.42 eV at room temperature, proving the potential of the approach for tracking charge dynamics also in these technologically highly relevant materials that previously have been inaccessible to attosecond science.