In April 2013, Mrk421 underwent unprecedented flaring activity, densely monitored during nine consecutive days at very-high-energy (VHE, E > 100 GeV) by MAGIC and VERITAS (with gamma-ray fluxes beyond 15 Crab Units above 800 GeV), in the hard X-rays by NuSTAR, in the soft X-rays by Swift-XRT, and by several optical and radio facilities. The high sensitivity of the instruments involved, together with the 43 (20) hours of strictly simultaneous observations in the VHE and X-ray energy bands with NuSTAR (Swift), make this dataset a unique opportunity for unveiling the highly energetic emission down to sub-hour timescales. In the present contribution, we report on the detected intranight variability, which could be decomposed into a fast (sub-hour) and slow (multi-hour) components that evolve differently across the various energy bands probed, showing a large degree of complexity in the relations between the emission at gamma-rays and that at X-rays. We will also discuss the consistency of the observed multi-band variability with theoretical scenarios where many blobs of magnetized plasma containing energetic particles are formed and accelerated in magnetic reconnection layers in the jet of the blazar.