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.
The Super NES Addams Family game is kind of tough, but there are extra lives pretty much everywhere to help you brute-force your way through it. Even on the Game Over screen.
Once you lose all of you lives, you have the choice of continuing or not.

But, instead of going through the 'Continue' door, you could just keep walking to the left and off the screen to find:

One of the many hidden rooms crammed into this game. This one gives you four extra lives that you can take with you to try and complete the game with.
And the best part?
If you lose all of your lives again the ones in the hidden room here will come back. So make sure you collect them every time... you'll need them.