Mrk 421 showed an unprecedented X-ray flaring behaviour in 2013 April 10--17 when the consecutive outbursts by a factor of 8--16 were observed in the 0.3-10 keV and 3-79 keV bands, and it became one of the brightest objects in the X-ray sky. During these events, the source was also very active on intraday timescales with fractional variability amplitude of 2-47 per cent, and showed the flux doubling and halving time scales of 1.16-7.20 hr and 1.04-3.54 hr, respectively. We have revealed up to 20 cases when the flux varied with 3 sigma significance within 1 ks. In this period, Mrk 421 also underwent the most extreme X-ray spectral variability ever reported for BL Lacertae objects. The location of the synchrotron SED peak moved from about 0.1 keV to almost 20 keV. The photon index at 1 keV and curvature parameter showed the ranges a=1.68-2.83 and b=0.09-0.57, respectively, and varied along with the flux on diverse time scales down to the intervals shorter than 1 ks. While the X-ray outburst were accompanied by very strong TeV-flares, the source was relatively less active in the radio-UV and GeV energy ranges.