Chao Container #1
Shortly after the first checkpoint, you will encounter the first poles in the level that you can swing on. Instead of swinging on them, simply drop down to the floor below and collect the first Chao Container from the far corner.
Chao Container #2
Continue on in the level until you come to the spot where the Bounce Bracelet upgrade is/was. You will have to climb the high walls in front in order to proceed through the level. When you climb up to the hourglass, just look around to the right for the second Chao Container. It is hidden behind a metal box.
Chao Container #3
Requires the Mystic Melody ability. After running through a long, twisting tunnel with annoying ghosts that like to grab and bind you, you will slide under a closing door to find the third checkpoint. There is an ancient shrine positioned right next to this checkpoint; play the Mystic Melody to produce a chain of rings, and use the Light Dash to travel along these rings to a crane which pulls you up to a higher platform. It is very easy to miss the crane and fall to your death, so good luck to you! You will find a second ancient shrine on the next platform; again, play the Mystic Melody and travel along the path of rings. You will be launched into the air and you must be sure to land on the rail in front of you. It will take you directly to the third Chao Container.