Really like the character!
The style and execution is great.

Your "line of action" is not as strong as it could be.
This is because you have the passive arms sort of working against the focus on the active arms:



By changing the pose a little you can create a more singular and definite, therefore "stronger", line of action.
This works much the same way as composition in designing a static image to create flow and focus.
Focus should generally be directed to the area doing or about to do the most action.
So here we try to change the shape to be more directional:



Your original is 12 frames and my edit is 23:


It's not that huge of a difference but it could get away with less frames if you have major restrictions.
We are both using 3 delays 60fps.

Especially wondering about speed/ delays etc

Decreasing the delay fps will allow you to get away with more action.
More impact and motion can be added as it all happens faster and flows together better visually.

Increasing the amount of delay means less work.
The animation lasts longer with less drawings.
But "drag shapes" and "multi frames" will be less effective the more time they are shown.

Find a good compromise between your engine/time restrictions, the amount of work you want to do, and how well you need the animation to flow.
Animation with less action does not require as low of delays.
But could still benefit from it of course.

Go look at my edit in the Punchy punch robot fun thread.
That animation runs at only 2 delays 60fps.
This makes it much faster and more room to stuff in action and timing.
However it ended up being 134 frames.
It depends on what you want but generally people agree that less work is favorable, and higher delays can still be made to look really good even with lots of action.

To get more speed you can do whats called a "multi frame".
You can start by drawing all of the frames separately, showing the motion, just as you already have:


Then you can stack them on top of each other all in a single frame:


packing multiple frames together makes the motion happen faster, as they are all shown at once.
At a decent speed your mind will perceive it as a fast motion.
The stacked frame will also clearly show your line of action.

After getting a good idea of the motion, arcs, and line of action, you can stylize this frame.
There are many different ways of representing this visually.
Purely multiple frames, solid drag forms, particle effects, repeating shapes, blur, etc.
It just depends on what you want.

This is how I styled the multi frame in my edit:


Doing more passes you can add cool stuff like particle effects, lighting effects, etc to supplement the motion.
Action and Reaction go hand in hand:


For me pixel animation is all about re-use.
Make finished art.
A few key frames.
Get good motion just using the select tool.
Clean up.
Make another pass.

What you have is a really good start.
Play around, try variations and new things.

Are you twelve? Can we call them breasts? That's what they are.

Hey woah.
I take full responsibility for this.
It was me that used the word first in reference to my own art, making the term comfortable to others.

I'm actually quite fond of words and how they interact with each other.
Alliteration is one of my favorite things, hence my handle (P)ixel(P)iledriver.
Palindromes and rhymes are cool too.

While "boobies" is not alliteration it has repeating b's and o's.
So I'm comfortable with and actually entertained by such words.

I was even considering naming the new character Booby Bandit (alliteration yay!).
But felt that Bootie had a little more pun to it in terms or being a bandit.

What if new one had longer socks?

Variations are cool so I'll give it a try.

Piledriver's stubby little arms bug me - just don't feel right.

I enjoy a good rubber hose character.
But agreed they make even less sense now that I've slightly toned her legs.
A few variations from now I'll see if something else looks better.

How do you do your greyscale conversions?

Nothing too special really.
The luminance value of a color can be found by averaging the rgb components.
If we test what Graphics gale does with pure grayscale values in 24bpp we can see there is a slight shift:


This seems strange to me because 128*3/3 =128.
Not 126.
It's a slight loss but I'm willing to live with it.

I wrote a grayscale shader for last years project but didn't really think to check if it shifts the luminance or not.
I might dig that up later just to see.

Also just re-reading this I realized I might sound a bit harsh:

Recently I've been doing edits around here on animations, but that only helps so much.
Fundamentals, principles, and techniques will help people much more than me just editing their work and sending it back to them.

Not my intention.
Edits do a lot of good and I'm still happy to do them when I have time.

put some more time into this:





A simple single image animation pass.
I'll end up doing a few more to figure out what I want to animate.

I'm a bit bothered by the lack of volume of the hair on the side with the secondary light source

For sure.
Not completely satisfied with the final hair update.
Some of the shapes are kind of blah.
A few of the older ones, like the one below the last, are more appealing to me.
Adding 1 darker color balanced the grayscale closer to what I want.
But dropping the lighter bounce color also took something out of it.
Will mess with more next time.

only thing thats bugging me is her chest, I think old robotic one looks better

Yes I also have strong interest in boobies.
No joke.
There are many different ways to draw them.
The robot style isn't too bad and with some refinement could work.
Playing around with different forms i decided to go with something softer.

also crown looks very cool but it seems somehow sideways to me

Agreed its a bit anti-gravity.
I like the cartoony feel of it being unrealistically tilted.
But I don't disregard the fact that something else could look better.
Tried some other stuff but haven't made a decision yet.

Thanks for crits!

A big thanks for help, but... I didn't understand any of those things. Would you mind explaining in a better way?

Admittedly the link I gave you lacks visual examples.
Since animation is visual it doesn't always help to read about it in words.

I searched around for a video and this is the best thing that I could find:
http://www.youtube.com/watch?v=xqGL1ZLk3n8

It's straight forward, short, and isolates each example without other distractions.
Unfortunately even though the animations are nice they are still lacking in teaching the technical skills to achieve each principle.
They only show you.
They do not show you how.
The description states "Designed as a memory aid", so it assumes that you already know what each one means.

The 12 principles themselves are not ALL there is to animation.
They are just a good place to start.
Many more tricks and techniques exist.
I can't seem to find any information about them on the internet.
But of course better material may be out there and I am just not finding it.

Search around and see what you can dig up.
You will find TONS of examples.
It's not that I think they are bad quality.
Although some of them are misleading or completely wrong.
I have just been unable to find any sources that are similar to the way that I was taught animation.

If you are REALLY REALLY interested I can cover maybe 1 topic a week (or less depending on how much work I have).
There's just no way I can explain it all in 1 post.

However if you are more interested in just small pointers for this specific animation that's cool.
But it may be difficult to apply without a good understanding and practice of the fundamentals.

Also Phlakes and rikfuzz both make solid points.
Keep their advice in mind as you work.