The first Metal Slug, to my knowledge, doesn't have a debug menu like the rest of the series, so therefore you have to use alternate methods to access these. Or just be a lazy ass and use the save states I slaved over to make.
What you'll need is Cheat Engine, and the patience to complete a few levels first, though it's not like the game is long, and make save states of each level (not necessary, but just helpful). In the first level and first scan, make your scan type "Unknown initial value," and once you reach the next level, make your next scan's type "Increased value by 1," and repeat until the results slim down. The level value should be like 16711939 or something among those lines. Just to be sure you've got it, decrease the value by one (be sure to freeze the value with the tick box) and beat a boss; if you're sent back a level, it works! If nothing's changed, then continue looking about until you get it.
With your level value, here's a list of all the areas you can visit! Of course, due to not actually checking, some of the mission values are probably wrong, but no big deal.