How do you control 130-size DC motors with an Arduino (seemingly 20A DC motors)?
The motors only go in one direction so you don't need an H bridge. Just use a logic-level power MOSFET such as IRL3103, which can be driven directly from the Arduino. To use N channel FETs you will need to change the circuit so that the motor common goes to battery positive rather than negative, but this shouldn't be hard. 

You should also put a diode across the motor to prevent voltage spikes from damaging the FET, and a Gate resistor to avoid high frequency ringing. The circuit might go something like this:-







simulate this circuit &ndash; Schematic created using CircuitLab