Heavier characters tend to excel at this challenge since they survive longer in the final battles. Wario was my first character to beat this challenge (and the 9.0 no customs in a separate run.) I later found DK to be even easier, so consider trying one of them if you haven't already. I didn't even need to modify either of their special moves since their default move sets worked just fine.
My approach is different, though. I prefer going in with my strongest DEFENSE equipment, plus an auto heal item. Why? The problem with taking the high offense approach is that you sacrifice defense to do so. Sure, the all offense approach can be faster in general, but it is riskier, and can add to the frustration factor if you make a mistake or mistime a move, which is easy to do. But with the high defense approach, you mainly sacrifice speed, and that generally is not an issue.
Wario completely nullifies his speed penalty from the defense equipment with his bike. Your speed while riding the bike is always the same, regardless of how high or low your speed bonuses/penalties are. Take advantage of this as often as possible. In group battles, and especially the Mii battle, you can spam his bike and wheelies, but just be careful using those on smaller stages. Even if you aren't spamming the bike, it still makes a very effective escape against large groups, and obviously it makes for an easy recovery back to stages, regardless of your speed penalty.
After you defeat the hands, immediately spawn the bike, turn around, jump off, pick it up, and carry it to the very middle of the stage. You'll have just enough time to pull this off. As soon as you can visibly see the Master Core's head, throw that bike straight up. It will bounce off the top of his head and do a great deal of damage, giving you a head start. Wario's neutral aerial deals multiple hits of damage, so use it often against most forms. Repeat this tactic after each of Master Core's forms, bringing out the bike, and using it as a heavy projectile as each form is initially spawning. I usually save the Wario Waft for the swords, but just be careful not to be too high into the air when you let 'er rip!
After defeating all of Master Core's forms, the bike will once again be handy for speeding through certain portions of Master Fortress. It also allows you to drive over acid unharmed, but just beware that abandoning it on acid will not cause it to break, making it difficult to retrieve. Fortunately when you scroll it away far enough (or wait long enough) you can bring out a new one as needed. Wario's chomp is handy against some enemies in the fortress, plus you can use it to heal when you eat your bike, or preferably its remains. Use a fully charged smash (or a couple good aerials), and then a Wario Waft on the second and fourth targets for an easy victory.
And if Wario doesn't suit your needs, DK's up+B is very handy against most of Master Core's forms. And obviously charge your punch between forms for an easy head start. You might find his raw power to be more handy (and quicker), but I find Wario to be more fun. Good luck!