Monitoring equipment should draw as little power as possible from your battery.
I like altosack (Dave's) post #5 best.
Looked up AVR ATiny861, like he says has 20x gain diff amp built in.
Look over the Data Sheets states in section 19.8.3 or page 153.
Set as bipolar mode, discover direction of input, then set up the differential channels as unipolar with the correct direction for the full range.
As mentioned; over sampling effective resolution enhancement can be achieved.
4 times over sampled get one extra bit. Search on ENOB for more info.
Sample 4 times, average result, now resolution is one bit more. 16X = 2 bits etc.
Remember resolution and accuracy are NOT connected in an ADC. The accuracy remains fixed, just have more bits to play with!
I drew up the opamp, but after reading Dave's post figured it was the best way to go.
Have fun,
Scott.