Fiber supercontinua represent light sources of pivotal importance for a wide range of applications, ranging from optical communications to frequency metrology. Although spectra encompassing more than three octaves can be produced, the applicability of such spectra is strongly hampered due to coherence degradation during spectral broadening. Assuming pulse parameters at the cutting edge of currently available laser technology, we demonstrate the possibility of strongly coherent supercontinuum generation. In a fiber with two zero-dispersion wavelengths a higher-order soliton experiences a temporal breakdown, without any compression or splitting behavior, which leads to nearly complete conversion of input solitonic radiation into resonant nonsolitonic radiation in the dispersive wave regime. As the process is completely deterministic and shows little sensitivity to input noise, the resulting pulses appear to be compressible down to the sub-cycle level and may thus hold a new opportunity for direct generation of attosecond pulses in the visible to near ultraviolet wavelength range.