Singling out a game on a GBA or earlier system (one without a filesystem) is very hard to do effectively. Making it boot to a given screen/game is usually far easier though seldom done, there are some oddities (something like the phantasy star collection on the GBA would have to be approached slightly differently) but for the most part it should not be that hard.
If it is a straight up emulation of a game (as happened on a lot of Wii virtual console stuff, also a lot of what sega have done over the years) then it is more viable to extract a game. I will note quite a few devs have somewhat odd ROM formats compared to scene and whatever.
Equally if it is a 2 in 1 game then most of the time you will be told to just get the originals, if for not other reason than a lot of those ? in 1 games are 256Mbit which makes things harder to fiddle with on flash carts and rarely fix bugs or add anything new.
Anyway the very first GBA assembly hack anybody really does is finding the binary, other than a few oddities (like the phantasy star collection mentioned earlier) it is quite easy and works the same for basically every game. I reckon you are looking at doing something similar to that, or possibly similar to those doing an scene style intro for a game (wait for the game to set itself up and then jump somewhere else, in this case to the start screen of the secondary game).
The first bytes in a game are the first instruction run by the GBA. This is usually a jump to the end of the binary, in your disassembler there will some instruction some 8 or so after that first jump lands to something in the 08?????? region. That 08?????? region is the binary proper. What will happen at some point after the menu is it will jump to the game you selected and that will be done with a jump to somewhere. Find this somewhere and make a jump to that happen earlier in the game (like just before it would have shown the selection menu) and you have your hack.
There are a few variations on the theme that some might do (mainly playing a macro or subverting button presses to always end up at the same thing) but first of all I would go for the method I just described, it should work and if it does not (sometimes a selection screen is more than a selection screen, just like a FMV can mask a load screen).
I am waffling. The short version is you are going to need basic assembly (know what a jump is and the basic ideas of assembly and program IO) and tracing skills (basically
http://www.romhacking.net/documents/361/ ) to try this.