The pixelation is created by making the Camera render to a Texture, then down scaling it to the size of the Gameboy!
Other effects I did to make sure it looked like a Gameboy:
- Capped frame rate to 24 fps
- Capped frame rate of particle systems to 8 fps with custom script
- Prevented soft shadows with a Shader that limits the color range of an object's lighting (unlit + clamped gradient of colors)
- Shader that limits the colors of a Texture to 4 colors, and replacing those colors using a Palette texture
Hope that gives a good idea of what you can do to get these effects!