The fastest you can sample is limited by the ADC clock, which can be as fast as the main clock frequency divided by 2, or 8 MHz. Now, at that sampling frequency your results will not be accurate! In addition, the datasheet says the ADC clock should not exceed 1 MHz (I'm guessing results will just be ridiculously wrong beyond that point). The "recommended" ADC clock frequency to meet datasheet parameters is 200 kHz or less (many of the ADC parameters are specified at 200 kHz). Another parameter of note is the "input bandwidth", which has a typical specification of 38.5 kHz so (according to Nyquist's theorem) there's no information beyond 77 kHz of sampling (though it is beneficial to sample faster than that if your signal truly does have spectral content up to 38.5 kHz).OK, so with that out of the way, let's say you settle on 200 kHz, that means you are sampling data every 5 microseconds.
This is about 100kbit/s, just beyond the capability of serial with baud rate of 115200.