As stated, you need to go talk to whoever set the requirements for your measurements. The dynamic range and precision required are just absurd.
Just for rough numbers, let's say your current range is 5 mA to 50 A. That's 4 orders of magnitude. If each current measurement must be accurate to .1%, that requires a system resolution of 5 uA. 50 A divided by 50 uA is 10,000,000. That is a 24-bit dynamic range. Trying to get this level of accuracy is enough to boggle the mind. At the least, keeping a shunt at a constant resistance (to within 0.1 ppm!) over a current range like this is mind-boggling. Think about self-heating for a bit. Hint - it varies as the square of the current. Think about how this affects the resistance of the shunt.
Much more reasonable is to consider exactly what range of currents will be encountered in a discharge cycle, and more importantly to establish just exactly why you need 0.1% accuracy. A 10-bit A/D converter will provide a nominal 0.1% resolution (with accuracy somewhat less due to nonlinearity), but attempting to extend this to calculate battery capacity to this accuracy is just silly. Among other things, battery capacity changes with discharge current level, temperature and age. Batteries are not precision artifacts.
Ordinarily, you would measure capacity based on a constant current discharge, with the test stopping at a voltage well above 1/2 the starting voltage. The test is then repeated for different current levels. To do otherwise is wasted effort. If you want to wring the last few electrons out of the battery, consider that, in a multi-cell battery this will inevitably cause one or more cells to become reverse-biased, and this is most definitely not good for the cells.
If you do this (constant-current discharge with a fixed cutoff) then a 10-bit measurement of the voltage and the current will provide a nominal energy resolution of about 9 bits, or ~.2%. For each different current level you can vary the shunt resistance to get the peak current measurement near full scale of the ADC.
Even if you decide to try for a full discharge of the test cell, keep in mind that, once you're below about half the original voltage, the time left will be (relatively speaking) very small, and inaccuracies introduced by limited ADC resolution will have only a very small effect on total accuracy.
And finally, if you really, really must try for this accuracy, you will need to pay extraordinary attention to the accuracy of your charge cycles. Extreme consistency will be the key, with absolute accuracy of charge current and temperatures required. Plus, you will need to provide some way to guarantee that each cell is (in absolute terms) discharged to the exact same level before starting a charge cycle.
Here's the relevant bit of the datasheet:
Footnote 2 is "Operational at VREF = 0 to 0.3 V, but accuracy is degraded". This implies you ought to avoid anything that needs a comparison threshold (the VREF value) below 0.3V. Since the amplifier has a gain of 20, this works out to a shunt voltage of 0.015 volts, which is above your shunt's expected voltage.
The really significant figure, though, is the SO offset voltage, which averages 50mV but can be as high as 250mV, and is likely the reason they don't suggest really low reference voltages; with a 300mV reference voltage, the amplifier's offset voltage could account for up to 5/6ths of the limit current - meaning your nominal 3A cutoff could be 0.5A, or 5.5!
I'd suggest scaling your shunt resistor so it gives the same output voltage as their example; for 10A limit, that means you'd want a 15 milliohm resistor. This will result in 1.5 watt heat dissipation; you'll need a relatively chunky resistor, but 2-3 watt resistors are easily and cheaply available in SMD packages.
Best Answer
In practice it is very difficult to get that kind of accuracy (0.01A at 50A is 0.02%) but it isn't necessary. 0.01A resolution is useful at lower currents, and is not difficult to achieve. I did it with a 0.001Ω shunt, precision op amp, and an MCU with 10 bit ADC.
Voltage will sag as the battery discharges, so to get accurate efficiency you need to measure Amps, Volts, rpm and torque simultaneously. However all these readings will have ripple, so they should be averaged over a period long enough to integrate the variations that occur at motor commutation speed.
With all the error sources combined you will be lucky to get better than 1% efficiency measurement accuracy, so don't worry if you can only get a current measurement accuracy of 0.2% (0.1A at 50A).