You need to know the peak current demands of your motor circuit before you can solve this problem. If you have a digital multimeter you can measure the constant current, and make a guess at the peak current. Put your multimeter in series with the motor driver and operate it at full power. The peak current may be as high as twice the steady current of the running motor. Also check the current with the motor under heavy load.
Then you need a power supply that can put out that much current, plus the current of your Arduino, without the voltage dropping below the minimum requirement for the Arduino voltage regulator (~7 volts).
What kind of batteries are you using? If you put 6 C cells in series you'll get 89 volts and pretty high peak current.