The fast travel portals are the doors located around the island, to start using them you will first need to unlock them. To unlock the doors you will need to purchase the keys from Hermes at friendship level 1, then use the fruit that you pick from the bushes to trade each key with Hermes.
Your first door will be in the starting zone just after you get off the boat, it's the stand alone door not the door to the building.
Once you have found the door walk up to it and use the required key for it, again you can buy each key from Hermes so farm fruit to trade with him if you're missing the one you need. After opening the door you can now freely walk inside and it will port you to the portal hub just south of Ora the statue in the centre of the island.
To actually gain this achievement, walk in and out of the portal continuously back n forth until it pops.
If you need more help with this you can follow my video guide below which begins at this achievement: