Nonlinear pulse compression based on the generation of ultra-broadband supercontinuum (SC) in an all-normal dispersion photonic crystal fiber (ANDi PCF) is demonstrated. The highly coherent and smooth octave-spanning SC spectra are generated using 6 fs, 3 nJ pulses from a Ti:Sapphire oscillator for pumping a 13 mm piece of ANDi PCF. Applying active phase control has enabled the generation of 4.5 fs pulses. Additional spectral amplitude shaping has increased the bandwidth of the SC spectra further leading to nearly transform-limited pulses with a duration of 3.64 fs, which corresponds to only 1.3 optical cycles at a central wavelength of 810 nm. This is the shortest pulse duration achieved via compression of SC spectra generated in PCF to date. Due to the high stability and the smooth spectral intensity and phase distribution of the generated SC, an excellent temporal pulse quality exhibiting a pulse contrast of 14 dB with respect to the pre- and post-pulses is achieved.