An 80W 350-2400nm monolithic supercontinuum (SC) source is reported. The high-power SC is generated in a uniform multi-core photonic crystal fiber (PCF) pumped by a 1016nm pulsed fiber laser. The specially designed PCF has seven 4.5μm diameter cores, a 0.85 air-filling fraction, and a zero dispersion wavelength (ZDW) of 991nm. The 1016nm pulsed laser delivers up to 114W average power, which is believed to be the highest currently reported for picosecond fiber lasers working below 1020nm. In order to ensure a robust and compact all-fiber structure, the pump laser is fusion spliced to the PCF using a selective air-hole collapse technique, achieving an ultra-low splicing loss of 0.2dB despite the severe mode field mismatch. The proximity of the pump wavelength to the ZDW of PCF leads to enhanced visible generation. The output SC has a high spectral density of up to 108mW/nm (at 580nm) and over 50mW/nm across the entire visible waveband. The achieved short-wavelength edge and high-spectral-power density in the visible region, to the best of our knowledge, are the best results reported for high-power visible SC sources.