So, the goal here is to answer "They call me Joe" at every opportunity.

The very first chance is when you wake up at the doctor's surgery and get to talk to Odie during the intro.

The next twelve can all be achieved pretty quickly, as soon as you're able to visit the town yourself and wander around.

Melanie

Mikey

Karen, the Town Hall Receptionist
Worth noting, the town hall is only open for an hour every day, between 12 and 1. If you miss it, just check back tomorrow.

Christine, the Barn Lady

Marco, the Ship Salesman

Harry, the Bartender

Ed, the Carpenter

Felix, the fishing dude

Santiago, of the Fishing shop

Steve, the Marketplace Akuba

On your 5th day on the island, you'll receive a letter from Nash.

Head on over to their hut and knock on the door. They'll pop out from behind a statue and you can say...

Followed by

The final person you can be all cool and mysterious to is Ben, stuck at the information desk in the Akuba village.

To get there, you'll need to speak to Steve - the marketplace Akuba - about crossing the bridge. You'll haggle a little over a lifetime pass and get a very deep discount. Once you've made the 1,000 gold and bought the pass you can cross the bridge and impress Ben with your mysterious ways.

You're done! The most mysterious Joe you can be.

But wait...

There are a few other people you can greet mysteriously but they don't count for the achievement. For completeness they're included here.

The gravedigger

Emilia

Cheers!