Vss must be grounded. With your current configuration, neither Q5 nor Q6 can conduct current, since their source leads only connect to the IR2125.
And controlling motor direction is easy. For one direction, keep HA and LB low, HB high, and apply your PWM to LA. For the other direction, keep LA and HB low, HA high, and apply PWM to LB.
And, for what it's worth, I really doubt that your gate resistors (R6 - R9) need to be 1 watt units. Not at 30 kHz.
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.
Best Answer
It might be fun to implement your own H bridge with external MOSFETS, such as the P channel FET that you linked to, plus N channel FETs for low-side with similar parameters.
You would have to implement a lot of protection measures though with discrete components that it might be better to find and implement a circuit which external switches but based mainly on a H bridge controller IC. The controller IC will have push/pull or charge pump MOSFET gate drivers for hard and fast control of the external MOSFETs, meaning you will waste less heat, and some have the option for current sense resistor feedback for over-current protection and other nice features.
Make sure you include clamping diodes to deal with back EMF.
Of course if you have little experience, it might be better to first make some simpler lower power H bridges first, and then work up to a nice big fully controlled high power one.
You may also buy motor controllers (for quite a lot of money) and save yourself some time and issues with testing. You show Sparkfun as a website in your link, perhaps check out the products available at Pololu's website, there are some nice motor driver solutions there.
You may also consider trying to change the motor you are using, to a 24V or 48V motor, to half or quarter the amount of current used for the same approximate 'power' output. Current is the killer, in terms of heat and nice explosions, so trying to reduce the amount of current to something less crazy would be something to look into for your project/design/thing.