by the way i would like to point out that burning a hole with your soldering iron is not a good move, you will make some horible fumes, remember the gameboys are made in the 80s before health and safety was "the new thing" and so they give off some pretty toxic fumes.
also you will ruin your soldering iron. the iron is made of a copper tip that is coated to protect the copper, if you damage that outer layer you will find the copper inside starts to fall apart.
how i make holes is:
start with a dremal-like rotary tool, they are very cheap and easy to come by and have loads of useful attachements like sanding shapes and cutters, they are great for cutting straight lines as well as holes and the sanders are good for just removing that last bit of plastic at the bottom of something. they are well worth it so it is worth spending a bit of money, i have had cheap ones before and one actually melted itself in half!
once you have got the hole where you want it, make the hole larger by a slightly larger drill bit in either a hand powered drill or battery drill. keep stepping up the drill bits to the size you want. this will help to keep the hole neat, and stop the plastic from cracking etc.
then you can use a round sander from your rotary tool, or a counter sink bit for your drill, to indent the hole to make it look a bit neater.
i used exactly this same routine to cut some extra button holes in my SP, see pic: