What should be the V specs of a step down transformer for a 10amp car battery charger
Most battery chargers that are a simple transformer and bridge rectifier DO NOT fully charge a battery. 
With a simple setup such as this the variations in line voltage would (and do) change the voltage output. 

You need to:


Decide the highest voltage you want to charge the battery to. I would recommend you select no higher than 13.8V.
Select the bridge rectifier you want to use (capable of 10A) and find out the Vf of the Diodes in it. You will lose 2 * Vf, so if your diodes have a Vf of 0.8V @10A for example you will lose 1.6V across the bridge rectifier. To get 10A RMS into the battery of course requires much higher peak current flow, so you will need to select a bridge that can support at least 25-30A peak. (You can read about conduction angles in bridge rectifiers if you like)
Using your charge voltage and diode drop you can now understand the PEAK voltage to be delivered by your transformer. In my example here that would be 13.8 + 1.6 = 15.4V (ignoring any other losses that exist in cables or transformer). Converted to RMS that means you need a transformer with approximately 11VAC. 


That is a very non-standard transformer and does not take into account the terminal voltage drop at high current or any other losses.
How successful would this be as a battery charger? At best it would be hit and miss. This type of ultra simple charger is also easily overloaded since there is no method to detect over-current. Connecting a flat battery may result in much more than 10A RMS which may overheat and damage your transformer.
In addition you really should have a battery charger that is short circuit proof and this certainly is not. A short on this would blow the primary fuse (assuming you are sensible and have one).