Is it possible with a Supercard SD to run GBC games normally (without using goomba) with a GBA? I can't seem to get it to work, and the game I'm trying to play (Shantae) doesn't run well in Lameboy and runs horribly in goomba.

 

Right, you cannot run GBC games natively without a dedicated GBC flash cart, which would be very difficult to find nowadays (not to mention expensive as heck).

Try the latest WIP build of Goomba Color, which has better graphical accuracy. Instructions:
1. Grab the Alpha 6 download from http://www.pocketheaven.com/boards/viewtopic.php?t=3280 (this is the one the Supercard SD uses, but includes the builder tools as well).
2. Replace the goomba.gba file in there with the updated WIP build from http://www.dwedit.org/dwedit_board/viewtopic.php?pid=1740
3. Follow the instructions at http://wiki.pocketheaven.com/Goomba to create a compilation.
4. Patch it with the Supercard patcher (otherwise it will come up blank when you try to run it). Use whatever patching options you want, though I personally use as few as possible.

No clue if it will help with Shantae, but it helps dramatically for GB Donkey Kong games.

 

This probably won't help too much, but try the following:
1. Press L+Start to disable the speed limiter. If it's not already fullspeed, this probably won't do anything.
2. Mess with the GBC Double Speed setting in the options menu (press L+R to access it).