Is there anyway of basically enhancing the soundtrack of this game, to make it less ... "crap" quality?

For example, here's the "Bowser's Castle" theme from Mario Kart Super Circuit:
http://www.youtube.com/watch?v=MqrFVoyq5yE

Here are the same tunes but (slightly) enhanced -- the former much more so than the latter:
http://www.youtube.com/watch?v=KlIWvV1yt_8

Is there anyway of enchancing the DKC3 soundtrack to something of that quality?

Nope that first link you showed is probably the best version of the "original" song that you'll get your hands on. The second link is i believe from a throwback GBA Bowser's Castle track in Mario Kart Wii which has remastered music, only for that specific track though.

Well that sucks, because it'd be much nicer to be able to listen to the soundtrack of this game. So, there's no way of making it less muffled, i.e. make it clearer?

No. GBA quality is what it is.

Which is why this doesn't make sense:

DS released between November 2004 and March 2005
DKC3 released November 2005

Should've been a DS game. And MOST of all, the sound should have at LEAST been stereo. The mono sound just makes the already low-quality sound even worse.