Can anyone be able to trace the curve such as below image in Adobe Illustrator.
Such a task depends on how precisely you wish to follow such a curve with its (possible) irregularities, and how you interpret the (rather asymmetrical) width distribution and the colouring.
Fewer Anchor Points yield smoother and cleaner curves.
One interpretation would lead to seeing the curve as a short straight part from A, then a strong/sharp bend into a softer clockwise arc, then a rather long, narrow, and soft, S hape ending in B.
For that, you may use four Anchor Points with the Pen Tool:
1) Click A;
2) Click or ClickDrag where the soft arc starts, depending on your interpretation of the strength/sharpness of the bend (if you drag, drag from the direction of A);
3) ClickDrag where the arc meets the S hape (along the direction of the transition part),
4) ClickDrag B (along the direction of the very last part of the S hape).
The Spacebar is your friend: while you work on an Anchor Point, you may press it temporarily to move the Anchor Point about inbetween adjustments of the Handles.
Obviously, you may go back to adhust Anchor Points/Handles, but Undo may also be your friend.
Here it is in Illustrator CS2 format...let me know if that's what you were looking for.
This is great!
However, the path of the curve is a wrong and I am not describe it clearly.
Take a look at below image:
Do you mind to correct the curve path?
Also, I would like to see the handles so that I can re-create the curve by my self.
Presuming you have Illy to help you:
A) Bust click the Pen (Tool) in the Toolbox and start Clicking and ClickDragging on the Artboard, also using the Spacebar, and see what happens. You may start a new path by pressing the P key.
B) Lock the image and start redrawing on top.
You can do it.