If you ask me, this "You didn't put any effort into this" is a cop-out.  Clearly he did put some effort into them, or he wouldn't have completed 4 pieces, each of which look like something, fundamentally.  It's true they look simplistic and childish, but that just means he doesn't know how to make things look as they should.  They are expressive and creative in nature. 

How can you refine something until you know how it's supposed to look and why?  Sit a random person down in front of an advanced math problem with no guidance and you'll be lucky if they write anything at all down after 10 minutes of frustration.  That doesn't mean they didn't try.  Why do people expect newbies to art to be any different?

And that seems to be the main problem... you can't really do pixel art until you know art in general.  The suggestion to hit the books and tutorials is a good one, but where to start?  First, read up on art theory.  A good book is "drawing on the right side of the brain."  It talks about how you should learn to draw "what you see" rather than simplistic symbols you've come to associate with what you are trying to draw.  Also, look at tutorials concerning color choice, and definetly shading/highlighting tutorials.  As for what to practice... start by drawing, coloring, and shading basic shapes such as a sphere, cone, etc. that can easily be compared to references and reality.  Once you can do that easily, those skills will transfer over to the more complicated things like your jellyfish's head.

Try these two links for starters. . .

http://www.itchy-animation.co.uk/tutorials/light01.htm
http://itchstudios.com/psg/art_tut.htm

Gonna have to contradict CAG.  If you want critique on an animation, you really should post an animation along with the frames.  Also the arm's length is perfect as is.

You should also try darkening the outline, and adding contrast.

In the north/up view, there shouldn't be a line seperating the head and torso.  This is because the head doesn't extend far out past the torso from behind like it does in front.  Also, since the legs would be going under the body and towards the background, the raised leg should be darker and smaller.

For the front view, the leg that's on the ground should be shorter;  This is because he is stepping forward with his raised leg, so the ground leg is farther back by comparison.

For the side view, the head should be wider.  His feet need to step up off of the ground, bending at the knees.

Well, my first suggestion:  Put the frames into an animated gif.  An easy way is to just download something like "animagic" and paste the frames into it.  It's easier to judge an animation than a bunch of frames.

Second, take a look at this:  http://www.anticz.com/Walks.htm

Awesome alien-like dude, and nice colors.  I think the eye size difference is too much though.  Also, at that angle, perhaps the eye should be the end of the face, no blue skin between it and the outside.

You seem to have made the nose thicker than it was in the pic, on his right (our left) side, and his left (our right) nostril doesn't stand out as much as the photo..