After defeating the queen in the final battle, Ico is sent adrift on a boat while the credits roll. He eventually washes up on a sandy shore and you regain control. The very last segment of the game involves walking along the beach and interacting with Yorda.
In your second playthrough, during this part, you can find some watermelon behind a large rock on the beach. You must carry one to Yorda and interact with her while holding it to earn this trophy.