You must fish for Ayu in the competition. Go to the billboard, have your basket empty, raise your HP, and use fish eggs that you buy from the store. Go all the way downstream and fish where you see a blue person on the ledge in middle of the stream.
Frogs and insects in In The Stream
You can get frogs on the other side of the river from the village on the big grassy patch near the bridge. You can get insects near the C section behind the fisherman by the rocks.
In The Stream: Worms
You can find worms in three small grassy spots in a small alcove of trees just southeast of the waterfall.
Mountain: Treasure map
In the mountains, go to the southeast corner of the lake and talk to the boy next to a monster. He will tell you that Nushie is hungry. Catch a full basket of fish, then come back and talk to the boy. When Nushie is full, he will give you a treasure map which reads, "A man waits alone on a island with no bridge". Swim to the eastern island and examine the tree.
Treasure map in In The Stream
Talk to the lady near the well, and she will ask you to get her a Rainbow Trout. After you give it to her she will give you a treasure map (from the Jiza 30 paces east, 10 paces north, 5 paces west). Go under the tree by your house and dig to find the treasure. You must do this to enter the fishing competition.
Ayu in In The Stream...