Browse for the Parola library - does just that using MAX7219 chip.
Can do with 2 shift registers; 74HC595? Brightness will be limited due to current limitations of the parts, really need a high current buffer like ULN2803, or 8 NPN transistors, to allow sinking of current from a common cathode row while the anodes are all driven at once to allow 1 of 8 multiplexing. The anodes need current limit resistors allowing ~8mA of current to keep within the 70mA limit for the chip's power pin.