There are a total of 6 barnacles in the game. The first will already be roaming the beach on Plumpet Island. The next four can be found in each of the large overworld locations: Plains, Desert, Field, and Glacier. The final barnacle is obtained after completing the lure delivery side quest given to you by the trader in the forest glade.
Update: As it has been confirmed by several people in the comments, you can make this run with Gnart with the help of speed flower/seeds. I just found PAT to be the easiest method of completing this.