A TIP120 is already a darlington with a reasonably high beta... if you're having trouble saturating it with the GPIO output of an Arduino, adding another transistor is just going to raise the Vbe drop another 700 mV and make the problem worse, not better.
You don't say how large a resistor (if any) you are using between the Arduino and the base of the TIP120, but using a lower value there would probably help.
The ATMEL datasheet specifies the minimum tolerable voltage for a "High Level" output as 2.3V ... typical value is probably going to be never more than one diode-drop below Vcc - or 2.6 at the very best.
While the datasheet for the TIP120 says the maximum Vbe is 2.5 volts, a much more typical value is going to be on the order of 1.7V ... To drive the transistor into saturation, you're going to need at most 5mA , well within the current limit for a GPIO pin.
A solution that adds parts count, would be to invert your logic, drive the base of the TIP120 with 12V through a suitably sized resistor ( around 2K would be adequate ) and use a small signal PNP driven by the arduino to "turn off" the base current. Schematic forthcoming.