how to use arduino to detect an 8Mhz ultrasonic pulse using piezo disc as receiver?
In a word: no.

Let's crunch some numbers...  You want detail like an oscilloscope.  Okay...

My scope is 50MHz bandwidth and runs at 1 giga samples per second.

Drop that down to 8MHz with the same kind of resolution, and you get (1,000,000,000 * (8/50)) = 160,000,000 samples per second.

That's 10 times more samples per second that the clock speed of the Arduino, and it takes at least 1664 clock cycles to take one sample.

So, no.  You need a board with an ADC which can run in the hundreds of millions of samples per second. The Arduino can only run at just under 10 thousand samples per second. 

A slight discrepancy.

Even the Arduino Due can only get as good as 1Msps. I have seen MCUs with 15Msps theoretical maximum, but for the kind of output you want you would need considerably more. 

So no, there won't be a cheap development "Arduino-like" board around that will do what you want. There may be an expensive one with a very fast CPU, DSP, ultra-high-speed ADC, etc, but you won't be programming it with Arduino, and you most likely won't be able to afford it to just play with.