I think Lucky 1 and 5 are the only ones you can get through without pick-ups. 4 is 500 pts minimum.

edit: see video below. 

The pink canons you just gotta do your best. You can touch them when they are closed. I took a few hits just so I didn't have to destroy them. There is almost always a easily grabbed power up at the beginning of each stage. 
 

Here is how I did it.

Geez skinny, that's the boring way of doing it.  I just circle around one of them while dodging the bullets from the others.  Makes it more fun!
 

Did you ever 1cc 1943?
 

Lol. True, not the most fun way to get through. 
 

I made it to the fourth battleship on the end stage, but couldn't finish it :/ 

but perhaps you were talking to Bert. 

Hey bert, there were other sections of the game were there was no "boring way" around
 

True enough.  There were several sections that required some very tricky flying.

I also made it to the fourth battleship, but never went back to try it again.
 

Yeah, Bert seems so expert at shooters that I wonder if even 1943 is too difficult for him.

Even though the contest is long gone, I'm _still_ trying to beat Legendary Wings. I keep screwing up on the fourth stage. :/


 

I'm sure I could finish 1943 with another few attempts.  My brother and I tried playing through Legendary Wings back in the day to see how many times we could beat it.  I think we made it through ten times or so before we got bored and quit.
 

Haha, no wonder you did so well in the contest. You must have all of LW etched into your brain.

Ten times???
 

I'm confident I can finish 1943 with a bit more effort as well 

 

I finally beat Legendary Wings! Yea I know it's probably easiest shooter on the NES which is why I could do it. And it was no-death!

Conglaturation!  Yeah, it is pretty easy, and more difficult if you die at all.