have you searched for any LED shield to get an idea? like this shield: http://timewitharduino.blogspot.com/2010/02/dual-bi-color-led-matrix-shield.html
It seems like you don't have a good idea about Arduino capabilities and your project's needs; you should do a bit more research.
Mega328 can supply 25mA on a single port, but the ground and VCC pins can't do more than 200mA (more restrictions apply), so if you want to draw 20mA per LED, then you can have at most 10 LEDs driven directly from Mega328.
You can do this project using series of shift registers. You should do a bit more research and post more details of how you want it done. What are the LEDs setup and arrangement going to be? do you want to have matrix addressing or direct connection (would need more shift registers)?