How do you complete Robin's flurry attack challenge?

You must fight a timed battle of length < 3 minutes

Looking at "walkthrough videos" (that really aren't too helpful) both here and here, it seems they've both used rule sets that set the match time to be less than 3 minutes. This is confirmed to be necessary in the comments:

Just so everyone knows, I've tried this multiple times and it didn't work. I changed the time to 2:30 instead of 3:00 and it instantly worked. Give it a go if you've been having the same issue.

- MiLo ChaelPez

So even 3 minute matches are too much!

In addition to this, I'd suggest fighting against a Jigglypuff, as Puff is very light and so will be launched further from your attacks and be killed sooner.

From another comment, it sounds like you can even get away with turning the launch rate up to 2.0x and still complete the challenge:

what i did was i choose jigglypuff as the cpu and set the launch rate to 2.0, then i went to Dreamland and beat it there

- DoggoTron

If you're having trouble actually doing the Rapid Jab, we actually have a question on just that (for this character too!) here.