Bubsy Pilot used 9 old clips, that we're borrowed from Archive Film and even from NASA.

They we're used:

1.) When Terry and Teresa ask Bubsy "Why do you wanna test it (Virtual reality helmet), uncle Bubsy?"

     Then Bubsy explains why:

"Because I am brave.."

Then it shows the footage of a brave man, who stops cannonball by his stomach.

This is Frank Richards (1887-1969), who was an American carnival and vaudeville performer and mostly known for stopping cannonballs with his stomach

(source: https://www.youtube.com/watch?v=-bxd1EsVhI8) (more info about him: https://en.wikipedia.org/wiki/Frank_"Cannonball"_Richards)

"Because I crave adventure..."

Then it shows a footage of a caveman fighting with some sort of monster. 

We are not sure where this came from. So no source found for this one yet.

"Because, I need to go, where no bobcat has ever gone before.."

Then it shows a footage of an astronaut jumping on the moon.

This is of course from NASA. More specifically, the First Moon Lading from 1969 (Neil Armstrong)

(source: https://www.youtube.com/watch?v=cwZb2mqId0A)

2.) When Bubsy says "Let's be heroes and save the day!" to Arnold. Then he grabs Arnold's tail, pulls him over and explains, how are they doing to save the day: 

"Let's take a bull by the horn.."

Then it shows a footage of a man riding on a bull, then he falls down and bull beats him.

No source to be found for this one yet. 

"Let's beat the odds..."

Then it shows a footage of two men boxing underwater.

This footage was recorded in Silver Spring, Florida. Boxing underwater was some sort of tourist attraction in Silver Spring, Florida in the 1950s. 

(Source: https://www.youtube.com/watch?v=X65ZSgWedqM)

"Let's throw the course into the wind!"

Then it shows a footage of a man in some sort of test. 

This man was in the G-force experiment in wind tunnel (level 9 of 10), that was tested by US military. 

(Source: https://www.youtube.com/watch?v=q01WLM6RwSY)

3.) At the end, when Bubsy tells to Arnold, how to save the day:

"You gotta live on the edge.."

Then it shows a footage of a man standing on one hand on a roof.

No source to be found for this one yet. 

"You gotta go for the gusto..."

Then it shows a footage of a man ice-skating with a rocket on his back.

It was a test on Rocket Ice Skater invention. But it didn't work and he fell down. 

(source: https://www.youtube.com/watch?v=iCTRjK69Vq8)

"You gotta be a hero for crying out loud!"

And for the final footage to show, it shows a superhero flying in the sky.

It's a scene from the movie called: Invaders from Space (1965). It's a movie, that was edited for American audience of the 1957 Japanese short series called Super Giant.

(source: https://www.youtube.com/watch?v=gSNenmvNmZU, time: 1:02:15) (more info about it: https://en.wikipedia.org/wiki/Invaders_from_Space)

So they are some of the footage found, but not all of them. Six of them are found, but three of them are still missing.