Hi!
I don't post very often around here, but since the Game Boy has kind of become my specialty lately, I thought I could help a bit.
Now, first of all I'd recommend that you work with a program that lets you see the color palette you're using, because your picture has way more than 4 colors. I opened your pic in Aseprite and the palette viewer tells me you have the following colors in it:

You should probably index the image, so there's no chance that you use a different color by accident.
Also, your picture is the wrong size. The Game Boy screen was 160x144 px in size.
That said, if you want to achieve a true "Game Boy effect", you should probably take into account the following things:
- Game Boy sprites could only have 3 colors, since the fourth was used for transparency (there were ways to work around this, but they're more relevant to the Game Boy Color).
- The Game Boy screen was made out of 8x8 px tiles. All graphics were aligned to that grid. Generaly speaking, only sprites could get off the grid, so everything else (map tiles, windows, huds, etc.) should stick to it.
- There was a limited number of sprites that could be displayed on the screen at the same time.
Considering all of this, I recommend that you look at your picture with a 8x8 px grid layered on top of it. You'll realise that many things, such as the huds and the fountain tiles, are misaligned.

Also, the huds you've designed (transparent and layered on top of the map) would've been near impossible to make in a Game Boy. They would've had to be made with sprites, which would've taken up a lot of the game memory and would've left almost no space to process all the other sprites in the screen.
Instead, I'd recommend that you treat the huds as if they were tiles: that is, that you make them non-transparent and stick them to the top or the bottom of the screen. That's how games like Legend of Zelda or Kirby's Dream Land did it, because it was the most efficient and easily readable solution.

I could tell you more things, but I think this is the most important stuff you could change to make it look more realistic. I hope it helps.
Good luck and keep on pixeling!