Here's my WIP.

I'm pretty sure this is already completely over the limit for number of unique tiles Game Boy could handle, but oh well. Trying to give the impression of snow covered ground. Not sure how well it's working.
QuickSilvaLike the character sprites, and the wavy background effect is cool. Maybe you can mix the small blocks in with the large ones to add some interest to the platforms.
OpacusReally great job. The enemy ships could do with a reduction in smoothness. Put whites next to blacks in places to make the geometric forms pop more. Also, lose a color in the sprites if you want them to match the spec. Game Boy can only display 4 colors, and in sprites one of those colors is needed for transparency.
mattnessGood start. Since you're using a dark floor, you should be able to get away with using white for the skeleton's limbs instead of black.
ArneI love the background. I can't decide if adding more dithering and texture would help or hurt the piece. You could do so fun stuff with dramatic, gloomy lighting and the like.
KATThe furniture is not as visible in your version. Maybe use black dithered with dark gray to bring out the items and hand/pointer. You'll notice the artist did just that in the original version.
vpkThat has a nice industrial sci-fi feel to it. I'm not sure if that would be possible on the Game Boy hardware, but it's a cool idea.
ArachneExcellent job! Not much I can see that needs improving. Funny enough, I just downloaded a speed run of that game last week.