the ground of the battery is the same as the ground of arduino.
Yes that is what it needs to be.
I would really like some more info, and the help needed to really understand this
Well it is just an idea of how I would tackle the problem, I don't have a circuit or anything.
You need a voltage controlled oscillator, that is a circuit who's output frequency is proportional to the voltage driving it. That would then be powered by one cell. So that is the main challenge getting that circuit.
This gives you a frequency proportional to the voltage of the cell. To get that down to the arduino you would connect it through a capacitor. That passes the AC signal but blocks the DC signal. You would have to have a zenner diode and series resistor to protect the arduino from any switch on transients, but you could then use the pulseIn() function to measure the period, and hence the frequency and hence the voltage. Because the capacitor blocks the DC you don't need to worry about the fact that the voltage is sitting up at a high voltage.
Another system that might work is to use a linear opto isolator. The main problem is that right out of the packet an opto isolator is not very linear. You can get them with dual transistors and use one to provide a feedback to linearise the response. Again it is just an idea.