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Precision ADC Measurements

I watched the videos on YouTube, about Driving SAR ADCs, and found a question: what to do when Vkick is orders of magnitude smaller than Vsettle? I'm looking to get 1/4 of LSB at the end of acquisition time.

I'm using a voltage divider, with a filter capacitor to drive the ADC. The ADC is the internal ADC of an microcontroller. The filter cutoff frequency is very low. It's a battery voltage measurement. 

The "# of T's" give me -4.6. What is the maximum frequency that i can sample de signal, without having capacitor related charge erros?

Schematic is attached.