Temporally coherent supercontinuum sources constitute an attractive alternative to bulk crystal-based sources of few-cycle light pulses. We present a monolithic fiber-optic configuration for generating transform-limited temporally coherent supercontinuum pulses with central wavelength at 1.06 µm and duration as short as 13.0 fs (3.7 optical cycles). The supercontinuum is generated by the action of self-phase modulation and optical wave breaking when pumping an all-normal dispersion photonic crystal fiber with pulses of hundreds of fs duration produced by all-fiber chirped pulsed amplification. Avoidance of free-space propagation between stages confers unequalled robustness, efficiency and cost-effectiveness to this novel configuration. Collectively, the features of all-fiber few-cycle pulsed sources make them powerful tools for applications benefitting from the ultrabroadband spectra and ultrashort pulse durations. Here we exploit these features and the deep penetration of light in biological tissues at the spectral region of 1 µm, to demonstrate their successful performance in ultrabroadband multispectral and multimodal nonlinear microscopy.