You should give more info about this....
PC specs, software used (emulator, recording device).
The PC specs are very important, because emulating DS games already needs a decent PC, not to mention to record it as well.
The file is so big, because *.avi files are RAW uncompressed footage, so that's normal.
You'll need a video converter if you don't want to edit the file and export it as a smaller compressed video file with a bit of quality loss, or use a 3rd party screen capture software if you want to get already compressed video files.