How do digital oscilloscopes achieve such high sample rates?
I presume they use Flash ADCs. These have the advantage that the conversion is immediate, while SA (Successive Approximation) ADCs like used in most microcontrollers perform an algorithm that requires a number of steps. A disadvantage of Flash ADCs is that they are rather heavy on hardware (an 8-bit ADC has 255 comparators), but most scopes don't have very high resolution. (Analog scopes often were 3% accurate, which translates to 5 bit.)