The entire chip has a limit of 200 mA, so some sort of external switching will be needed. For example, transistors.
Do you need each LED to be individually addressable? (controllable)
You only have 20 pins which can be used to control stuff (D0 to D13, A0 to A5) so you may need some form of external control, like a shift register or port expander.
As for your battery requirements, a bit (lot) would depend on how often the LEDs are on. For example, if you only have half on at one time, that would halve the power requirements.