I got the same board in a ebay backup camera. It was very difficult to fit inside the gameboy shell but can be done.
I started by dremeling down the sides of the board as close as i could to the surface mount components without damaging them. You will notice i did grind through a couple of traces on the back of the board. Everything seemd to still work including the buttons so i went ahead and desolderd them.
The board still wouldnt fit so i had to extensivly dremel out the inside of the shell. This is where things get abit ugly, its very easy to heat the dremel bit up too much and end up melting through the side of the shell. In my case i rushed it and the shell shows a few blemishes on the outside.
As for the 5v conversion i solderd the 5v input directly onto the regulator pin shown in the above pic. It helped the screen flicker alot but wasnt completly fixed, thats as far as i got. Hope this helps!