Advanced ADC setup on Due (SAM3X8E) to increase precision
Generally speaking the input BandWidth of the analog signal is a major cause of noise in a ADC circuit as well as improper ground and reference generation and layout techniques.  Be very careful that ALL of the analog paths do not have any digital current return paths. Remember that at 12 bit for a 1.25V reference an LSB is ~300uV. I have not ever measured the SNR of the SAM ADC but I doubt that it is the specified ~60db (i.e. 10bit) unless absolute care is taken during the layout/routing.
Recommend:
1) Limit input BW to the correct channel ground. (well below Nyquist BW if possible to avoid alliasing)
2) Oversample if possible.
3) Insure low digital I/O of peripherals during sample period.