240siWe report on a multiband variability and correlation study of the TeV blazar Mrk 421 during an exceptional flaring activity observed from 2013 April 11 to 19. The study uses, among others, data from GLAST-AGILE Support Program (GASP) of the Whole Earth Blazar Telescope (WEBT), Swift, Nuclear Spectroscopic Telescope Array (NuSTAR), Fermi Large Area Telescope, Very Energetic Radiation Imaging Telescope Array System (VERITAS), and Major Atmospheric Gamma Imaging Cherenkov (MAGIC). The large blazar activity and the 43 hr of simultaneous NuSTAR and MAGIC/VERITAS observations permitted variability studies on 15 minute time bins over three X-ray bands (3-7 keV, 7-30 keV, and 30-80 keV) and three very-high-energy (VHE; >0.1 TeV) gamma-ray band...