How do I determine the Schottky diodes to use with my H-bridge?
The Intersil HIP4080A controller chip doesn't appear to need the normal "freewheeling diodes" that are sometimes seen in motor driving circuits.  The diodes in parallel with the MOSFET's in Figure 33, Page 14, are integral to the N-Channel MOSFET itself and not a separate component.  

If, for whatever reason you decide that you need to use freewheeling diodes, you would put them in parallel with the ones integrated with the MOSFET's.  I would recommend diodes with a reverse voltage of at least double your motor voltage and 1x, and preferably 2x of the stall current of the motor.  Since your motor is 12 volts @ 25 amps, I would recommend diodes of at least 24 volts and 50 amps.  These are not small diodes.  The diodes in the datasheet you linked to are not even close to handling 50 amps.

In Figure 33, there are two more diodes, CR1 and CR2, but the datasheet doesn't say how to spec these.  The diodes are located between +12v and AHB/BHB pins.  On page 4 the datasheet says that the absolute max voltage on those pins is 80v+VDD, and since VDD is 12v then the max voltage is 92v.  Therefore, without going through all the little details you'll need a diode that is spec'd for a reverse voltage of at least 92 volts.  

(Note:  I'm doing a very rough analysis to come up with 92 volts, and I'm being very conservative too.  If you get a diode that goes to 92 volts then it'll work.  It very well might work with a diode rated at only 25 volts, but it's impossible to tell just from this datasheet.  To be sure, you'd either have to get more info from the chip manufacturer, simulate it, or build it and measure the thing.)

It's also really hard to tell from the datasheet what the current ratings on CR1&amp;2 need to be.  It is mostly going to be determined by the values of C3 and C4-- values that they don't give.  Here again you'll either need more info from Intersil or you'll have to build it, measure it, and then change the diodes accordingly.  As a rough starting point I would go with diodes in the 1 or 2 amp range, but keep in mind that I could be as much as 10x high or 10x low.