-( Story required, cannot be missed )-
After placing the third tablet, Edmond will approach you over two days and, with his apprentices (should you have repaired their houses, otherwise this won't happen), he'll divine that the fourth tablet is in possession of the Harvest Goddess. The only problem here is that they do not know where she is. Repair more houses, and eventually, you'll get a cutscene in the town square where the villagers are discussing the legendary Blue Bird (a staple of the Harvest Moon franchise). For me, the cutscene happened with Melanie, Sally, Sam, and Michael. They say that the bird can only be seen at night on the beach of a sunny day. Blossom will come the next sunny day and greet you, letting you know that now's the time to strike. Wait until 6 pm and be at the beach (the scene will start automatically or any time you enter after this point). But all you'll have to show for it is a strange bird rock with an apple on its back.
Blossom will suggest you talk to someone who knows something about animals, which means Sofie and her kin (importantly, it's Gabriel). He'll tell you the recipe to make Delicious Animal Feed using your windmill, which you might need to repair next if you haven't already. The recipe for the feed requires 2 Flour, 3 Strawberries (or 2 if great), and 2 Milk (1 if better quality). Flour can be grown out of season, as can strawberries, but to get milk, you have to actually raise a cow. After you get the proper feed, the next sunny day Gabriel will come by your house and wish to accompany you to see the Blue Bird.
The cutscene will end with you meeting another Sprite named Woody, who has a request for you to get some Strawberry Jam. The recipe will be foreign to you unless you directly get it from a cutscene in Bastian's restaurant. The ingredients are one Strawberry and one Sugar (Sugar can be bought from Sam). Take this item to the Harvest Goddess Spring to meet with the Goddess, obtain the fourth tablet, and with Woody's help, restore the fourth light!
However, there is more to it than just that. What seems like the end is in sight is actually much further from the truth, as the cause of the storms turns out to be Gorgan, and another such storm whips up after some cutscenes follow placing the fourth tablet. Your next goal lies with Doc providing you the answer to the final tablet.
You shall also unlock this trophy through the progression: