Try changing his Side Special to Koopa Drift and his Down Special to Big Mechakoopa.
Koopa Drift will spin longer and rack up more damage. And release Big Mechakoopa's, then pick 'em up straight away and throw at your opponents.
From what I've experienced, a single opponent without Reflect has a hard time dodging Big Mechakoopa explosions, so you could try throwing Big Mechakoopa's at 'em over and over til you build up damage.
If they don't work, just grab all the items you can find and lob 'em at em.
Also, Vampire Badge helps make the challenge a little more manageable.