Recent indentation experiments indicate that wurtzite BN (w-BN) exhibits surprisingly high hardness that rivals that of diamond. Here we unveil a novel two-stage shear deformation mechanism responsible for this unexpected result. We show by first-principles calculations that large normal compressive pressures under indenters can compel w-BN into a stronger structure through a volume-conserving bond-flipping structural phase transformation during indentation which produces significant enhancement in its strength, propelling it above diamond's. We further demonstrate that the same mechanism also works in lonsdaleite (hexagonal diamond) and produces superior indentation strength that is 58% higher than the corresponding value of diamond, setting a new record.