The Adventures of Rocky and Bullwinkle for the NES is a pretty terrible game, but if you're determined to play it, I've got a shortcut for you.
First, start the game
Then, on Controller 2, press
B, A, A, Start, A, B, B, A
Done correctly, you'll hear a confirmation noise. You can then press the B button on Controller 2 to skip to the next stage.
If you skip the final stage (the second one with the painting) you'll end back up at the beginning, so you have to actually finish it if you want to see the ending
Or you could look below this line for the entire ending (spoiler warning, I guess)
Yeah, it's just the one screen.