Ok, if you just want to beat the 15 min melee and you don't care how, use DK. Position yourself under the the right or left lower platforms and face the center of the board. Hold down on the control and press B repeatedly for the duration of the challenge. DK will pound the ground continually and the wireframes won't stand a chance. Now, as the enemies blast off the screen, DK is pushed in either direction, so repositioning occasionally is important in avoiding being pushed off the board.

15 minutes of this was rather tedious, but I was able to beat this melee on my first try using this method. I suffered less than 150% damage and took out over 700 wire-frames.