The Explorer Extraordinaire trophy can only be obtained once you have unlocked all the islands in Dragon Quest Builders 2.
We are talking here mainly about islands, which are accessible to you only by buying a ferry or boat travel option. For access to the island you pay with Gratitude Points (hearts). The prices are different, for one island you have to pay 50 hearts, for another 300.
You will only get access to these islands after completing the main story on the island of Furrowfield, and then return to the Isle of Awakening. There, your carrier will tell you about these islands. In addition, on these islands, your main task is to study and conduct some research over a specified object. These are all sorts of things. Sometimes you have to examine and inspect a simple tree, a rock or even a new plant. For finding all the items that the game asks you to search for, you may get some cool rewards.