DeSmuMe

DeSmuME is a Nintendo DS emulator. It is also available as a libretro core for RetroArch.

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DeSmuMe is currently the best Nintendo DS emulator out there. It is far better than No$GBA when it comes to accuracy.

If the game is slow.

Enable the dynamic recompiler in Emulation Settings.
If it's still slow, you must be running on a toaster. It can't be helped. But try tinkering with things for the fastest settings you can find.
Use frameskip as the absolute last resort.

If the sound is distorted.

Synchronous mode is far less buggy. Method Z seems to work the best in most cases.

If the video is hideous.

DeSmuME's OpenGL 3D mode supports Multisampling Anti-Aliasing(MSAA). Turning it on helps the serrated edges of ultra low-res DS polygons and lines smooth out, appear to wobble less during movement, and retain their shape better when viewed from distance.
The only other real thing you can do is filter it. Make sure OpenGL and Filter are checked under Display Method.
Yes, filter it. Whether that is simple Nearest 2x or some pixel art scaling filter like HQx or xBRZ is up to you.
OSX version of Desmume also has support for multi-pass post-processing shaders and filters which Windows version currently doesn't have.
Leaving it native and aligning it to a CRT (Set to a 384 high resolution) is also an option, if you feel like going through the effort.

If the 3D is messed up.