Go to DK Theatre in your Mystery Menu and select the Intro Story. Press the "A" button to stop it a few moments after it starts. If you end up back in the Mystery Menu with absolutely NO music playing you did it right. (This will probably take a few tries as timing is critical.) Then wait about 45 seconds and start the End Sequence from the Mystery Menu. After the Banana Fairies enter the tunnel to DK Isles in the cinema, instead of playing the rest of the ending as it should, the game starts playing the Intro Story with credits rolling and the music for the ending playing over it!
The intro scene proceeds as normal, even with the credits constantly squashing themselves into view, but sometimes the scenes end sooner than they should, and sometimes the graphics don't render correctly.
This is just really messed up.
I think NOA should've done more testing.
Eventually, the scene will end with Donkey Kong in his treehouse and K.Rool's voiceover still going. You'll gain control of DK, but you can only swing his arm with the "B" button. You can't move or bring up the pause menu. Pressing "A" takes you back to the Mystery Menu.
WARNING: I do NOT recommend starting the game from one of your saved files after performing this glitch, as it could possibly have adverse effects on it. It's safe to do this glitch all you want from the Mystery Menu, but I strongly advise resetting or turning the game off before starting adventure mode again.
Special thanks and credit to dvdmth and David Wonn. Please visit David Wonn's Unique Glitches website to learn how to do a lot more fascinating tricks for this game (and lots of other games, too).