This is the same process as picking 10 and 250 fruits.
Start the game and follow the story and after 5 or so minutes in you will come to the statue that tells you all about the place and will help guide you along your way. Once you have been through all the dialogue with the statue the game will then start to produce fruit on all the bushes across the island. Simply pick 500 for this achievement.
Please note you will have to pick this fruit in the wild not from the plants that you grow later in the game.
Also note, shortly into the game you can save progress and pass time, if you pass time a couple of days then the fruit will respawn on all the bushes as the fruit naturally respawns every couple of days.
If you need help with this then you can follow my video guide below which should help with this achievement: