How to sample and hold on very narrow pulse?
A peak detector is something of a sample and hold that samples all the time, and holds the peak:



Follow the input with this, and connect the output to your ADC. Make C significantly larger than the capacitance used by your ADC's sample and hold, or follow it with a buffer, so the voltage across C doesn't sag as you read it.

Trigger an ADC reading just after the event happens, and when it's done, close the switch to reset the peak, or make the switch a resistor forming an RC time constant significantly longer than the time it takes to measure the peak but significantly shorter than the interval between peaks to accept a little error but avoid the need to reset the peak detector.