The NES Addams Family game is kind of tough, which means that you're going to be seeing this a lot:

But! Just like the Super NES game, you can just throw more lives at the game and brute-force your way through.

First, go to the title screen

Then press the following buttons on the controller:

A, B, B, A, Left, Right, Left, Right

If done right, you'll see a green letter C appear on the top-left of the screen

Now you'll have as many tries as you need to finish the game

And you're going to need as many as you can get.