In today's series of tests I used an ATTiny85 that would turn on an LED when a INT0 pin change interrupt occurred.  BBs were the test projectile used.

First prototype version:  Two pieces of aluminum foil with a piece of cardboard as both an insulator and to hold the thing up.  I didn't expect this to work too well due to the thickness of the cardboard. And as the test clip shows, it didn't.

I then added another layer of foil to the front and back.  This kinda worked, but not very well:

I decided then outright eliminate using the cardboard piece as the insulating layer and decided to go with something much thinner, parchment paper.  The cardboard now just served as a support.

Things worked much better:

A side effect of using such a thin material for the insulator was the two conductive layers would sometimes make a persistent direct contact after firing a projectile though the target. Perhaps adding another layer or two of parchment paper would help mitigate this issue.

It would be interesting to see if there would be any differences if a projectile was going at a much higher speed, say one fired from an actual firearm.  I could try borrowing one from a friend, but there is the issue of where I could conduct testing.  I'd rather not get unwanted attention from the local police for firing a gun in my backyard.  If anyone knows of something that can fire at a considerably higher speed than a typical BB gun that's not an actual firearm, please do comment .