Don't listen to these guys. The Advance rules those other handhelds.
Here is a link to somebody's guide to backlighting it. It's a little vague as there are no pictures and there is no mention of the shiny stuff behind the screen.
http://www.associatedcontent.com/article/980028/how_to_add_a_backlight_to_a_gameboy.html?cat=59#comments
You will also want to get a special tri-wing or 'Y' type screwdriver if you don't already have one. they are pretty cheap on ebay and other websites, just Google for 'GBA screwdriver' or something.
I haven't backlit mine yet and I am waiting for my screwdriver so I can open the thing, so I am not sure exactly what to do yet. There is a lot of talk on the internet saying it can't be done, but I think it's just hearsay, as nobody seems to be able to explain exactly why.
I think you can also get a backlit SP, take it's screen out and install it into the GBA, but I am not sure.
If I succeed, I will definately make an instructable and put a comment here.