Arduino Motor Control Circuit with Power Transistor and H-Bridge
You have the right idea using a MOSFET, but since your motor can draw up to 85A you need a more powerful FET. Also you must put a high current Schottky diode across the motor (cathode to +12V) to prevent voltage spikes when the motor is switched off, particularly if you are using PWM to control motor speed. As well as suppressing the back-emf caused by inductance in the motor windings, the diode also improves efficiency by recirculating current through the motor during PWM off time.

You should aim for a voltage drop of less than 0.1V at maximum normal operating current, so the FET needs an Rdson of 0.0025 Ohms or less. If a single FET can't do it then you can put several in parallel. Two STP180NS04ZC's in parallel might seem to be enough, but they have another problem - they need 10V on the Gate to turn on, but the Arduino only puts out 5V. You can get around this issue by adding a Gate driver circuit that boosts the PWM signal from 5V to 12V, or you can choose 'Logic Level' FETs that turn on with 5V or less. 

One advantage of a Gate driver is that it isolates the Arduino's output port from potentially damaging high voltages and currents (if the FET broke down from Gate to Drain it could put 12V into the Ardiuno, which would almost certainly destroy it). Another advantage is higher drive current, allowing you to put more FETs in parallel without compromising switching speed. 

Gate drivers are also essential if you want to make a bridge, because the high-side FETs need a higher voltage gate drive (exceeding the supply voltage if you use all N Channel FETs). You can make a simple gate driver circuit with a few bipolar transistors and resistors, or you can use an IC such as TC4427 or IR2101.  

At the high currents you want to switch it is probably better to make a bridge with discrete FETs rather than an IC. High current integrated bridges are usually very expensive, and if one transistor blows you have to replace the whole module.

For a bridge You don't want a schottky diode across the motor (since it would short out in one direction) but in this configuration the FETs' built-in body diodes are normally enough to do the job. You will want to add 200uF or more of low-ESR electrolytic capacitors across the motor supply to suppress voltage ripple, and you must be careful to avoid ground loops between the bridge and Arduino. You might even consider using opto-couplers to provide isolation between them.