An 80 W 350-2400 nm monolithic supercontinuum (SC) source is reported. The high-power SC is generated in a uniform multi-core photonic crystal fiber (PCF) pumped by a 1016 nm pulsed fiber laser. The specially designed PCF has seven 4.5 μm diameter cores, a 0.85 air-filling fraction, and a zero dispersion wavelength (ZDW) of 991 nm. The 1016 nm pulsed laser delivers up to 114 W average power, which is believed to be the highest currently reported for picosecond fiber lasers working below 1020 nm. 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 0.2 dB 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 108 mW/nm (at 580 nm) and over 50 mW/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.