A short ways into the Waterfall level, you will come to a room where you climb a ladder and then make your way around the room by hanging from rails to reach a platform with a switch. When you pull the switch, it will start a large gear turning and cause a big piston to start moving up and down. You need to use the piston and time your jump to reach a high ledge and exit the room.
You will exit to a grassy area with a water wheel at one end. Go to the left of the stairs and pull the switch to open the door to the room you were just in and let Yorda out. Now smack the tree right next to the switch with your sword to make a...coconut, or something...drop from the tree. Pick up the ball and carry it back into the room with the piston that you just exited. Go left up the ramp and set the ball down. Now push on one side of the middle section of the back wall to make the wall section turn, and open the way to a secret room.
There are two ways here to get the spiked club. The "regular" way is to go grab Yorda and stand on the glowing circle in the lower part of the room. This will make a "basket" rise from the floor in the upper part of the room. Now pick up the ball and go up the ramp to the upper area. Stand as far from the basket as you can, then step forward and throw the ball. Once you get the ball in the basket, the spiked club will fly in through the window. Exchange your sword for the spiked club and leave the room.
The "easy" way to get this is to first pick up the ball, take it up the ramp to the upper area, and then set it down inside the square of the "basket". Then get Yorda and stand on the glowing circle to raise the basket. The ball will then automatically drop into the basket and the spiked club will fly in through the window.
Note that the trophy may not unlock until you solve the water wheel puzzle and leave the area.