Just jump on top of it. Your weight will push it down.
Hop on the statue's head. You will sink it. The other part of the statue will appear on the right hand side. The mallet will be there. Collect it. Happy playing!
Sink the statue in the water at Dragon Cove by standing on it. The tail will rise and you can get the Mallet from it. (Move the old man to the right, near the first barrel, then use the mallet to ring the gong.)
Stand on it's head, it's tail will come up revealing a mallet.
in dragon cove
The dragon statue at Dragon Cove conceals a large mallet. Stand on it and it will slowly sink to reveal the mallet. Push the old man to the right, next to the first barrel. Use the mallet to strike the gong.
Dragon Cove. To get the mallet stand on it's head.
jump on it
At Dragon Cove, the statue is down in the water under the Trading Post. There is an old fisherman there who can help you find the Map Piece. (see related question)
The French shipped the Statue of Liberty in 250 separate pieces, making the transportation of the Statue possible.
You have to defeat him. He doesn't sink, but he runs off, and that is good enough for the Governor. Go back to see him and he gives you the directions to the treasure, and a shovel to dig it up.
You have to defeat ships and sea monsters and pick up the cargo that they leave behind when they sink.
I can see no indications of such in the Wikipedia Article.[1]