How does one perform this quick kill? I've seen it plenty of runs but I haven't come across any info on how to do it? Any help is appreciated!

As far as I know it has to do with skipping phases, this goes for a lot of bosses, one that I take notice of is Hilda in World 1. When you go over a certain damage amount in the phase it ends up actually skipping that phase, so you basically beat Beppi's 1st and 2nd phase in his first phase and has to play the second phase of beppi, so it ends up doing that, but gets stuck trying to process the 3rd phase and the boss kind of locks itself.

So obviously you'll be using WSG to get max damage. You want to push to about 1-1.5 cards on his first wiggle right as the fight starts, then turn around and throw spam as much damage into him as possible. Use all EX attacks and everything. If don't correctly, you do enough damage to skip his second phase which causes the fight to freeze and you just have to dodge the balloons/rollercoaster for the rest of the fight while spamming into him in the middle.

Here's a video showing how to do it. :)