Hello. I have a question. Is there a way to make the plastic cartridges?
Most people would probably buy a bunch of cheapo GBA games and gut them for their cases, however that is easier said than done than it was in years past.
To that end you have three main options, the approach you take varying with how many you want to make and in what manner, possibly also what quality.
1) 3d printing became something mortals could do a few years back. Depending upon the printer and method used the surface finish might need some work, and you might need to finish something by hand or in a machine. Everything from shapeways to your local hackerspace/makerspace or local people looking to rent their 3d printer out will do here.
2) CNC. Take a block of suitable plastic, cut away with a machine until you have something of the right shape and size. More materials available here than most 3d printers, surface finish potentially far superior. Some of the same sorts of things as above will do this, as will many machine shops. You can buy your own too for sometimes less than a 3d printer (just about any mill you find for the same price as a cheap 3d printer will probably be better than said 3d printer) to as much as you like. Few people and places will be offering rentals in my experience but you should still be able to find something.
3) Injection moulding is something that can be done at fairly low volumes, though you will probably want to be in the 50 range before it starts making real sense. People have done it for years in the miniature figures and low volume board games worlds and time has made it easier still. More limited than CNC for materials but way more than 3d printing will allow, and if done even vaguely well will be a better surface finish than a basic 3d printer.
In any case you will need a computer model of the case. I don't see one on
https://www.thingiverse.com/tag:gameboy_advance so you will probably have to make your own. The tolerances are pretty tight (see issues with GBA flash carts being too tight or losing connection) but nothing you could not do with a basic set of vernier callipers and a micrometer. Said tolerances are why I am not so inclined to point you at things like mould making using clay/cement/silicone/similar, though if you wanted to experiment then it is not an expensive experiment. If you have a manual mill then you could probably make one too but you probably won't and paying someone to make one for you will be far more expensive than buying anything other than a rare GBA game to gut for its shell, I don't tend to see them in schools any more either.
Some of the same people to have a 3d printer might also have a 3d scanner or touch probe but the former will only get you so far and if you are asking this sort of question then you will probably not find someone willing to let you use the latter.
Depending upon the procedure you end up using then you might have to build in allowances for the methods (you might have to lay a raft for the 3d printer, have a means to hold it down for the CNC, have sprue locations for the injection moulding) and possibly suffer the usual fun and games with setup of them or quirks with the machines. As you are not doing massive undercuts or anything like and wall thicknesses are low but still sensible you will probably be spared the really fun aspects.