Internet connectivity for the Arduino Due using AtmelStudio?
Well, your best bet is to import the arduino libraries in your Atmel Studio project. Then you'll be able to use existing code to connect to the "traditional" Ethernet Shield using SPI.

Though, the Sam 3X features an hardware ethernet that is not wired, unlike the MBed LPC1768… Sadly that's the ethernet PHY component you saw, but won't be able to actually use…