Here's the reference image that I used:

and here's my work (Outline only):

Can someone explain if am I doing anything wrong with the curvature lines ? I've tried to update it multiples time and that's my best so far. Thank you
Shade for curves, kill the lines.

Shading is a pixel artist's best friend (most of the time)
The reference art is using a common drawing method called Anti-Aliasing. This allows lines to appear very smooth, when in fact all it is doing is using black pixels of varying alpha levels next to each other.

To achieve smoother lines, try using some transparent black pixels around the "corners" of the lines you made and see if it happens to make your lines look a little smoother.
Made it more round without anti-alias.  photo 2014-072FYasuShy-00012FSkull_Roundification_zps00c692dc.png

Here is a tutorial page, there is a section called Jaggies that shows and explains jagged pixelated lines.
Super fast tutorial:

First, make your line art and clean it up to get rid of jagged lines. (See PsyRabbit's link)

Then, color and shade the way you like. Develop your own style of it.
Example: I use heavy outlines in my work

I suggest practice and practice some more. Post your work for critiques and comments.