Cheap trick : moved the first and third frame a pixel down to get a bob-like motion.
I find the frames in which the two feet are on the same level weird, generally speaking one shouldn't use the idle pose as an in-between frame for a walking animation.

Edit incoming ! I got the impression from your hood shading that you were thinking "I've got the front-view that looks fine, so I'm gonna rotate that and try to keep the same shading". Instead, try seeing the side-view as a different object and shade it from scratch, sticking to your lightsource. Some parts were also a bit pillowshaded so I tried fixing that too.

The second row is the same spritesheet from which I've removed one color that was almost the same as another.
Pixel art follows different rules than traditional art does : few well-contrasting values > lots of slightly different values that create a gradient.

Alright got it.
@thesydneylad actually I have seen mots of your attempts when you originally posted them, and I agree on the fact that they share the same issues. And clearly, never coming back to edit your own unfinished piece isn't gonna help you progress.
So either you feel like doing two pieces in parallel (and in the end, abandon none of them !) in an incremental fashion, or you feel like working on only one project for now, in which case you should take a break when you feel stuck, but always coming back to it so you can actually progress and not restart from scratch everytime.

"Smaller pose" = even less pixels, right ? So no, I don't think it'd help atm (again, this is my opinion, and I'm not an expert).
My take would be, for now at least, open a 50*50px canvas, and try redoing it from scratch, without being limited by a frame.

You asked for a more indepth critique, so right now, anatomically speaking :
- his whole silhouette is bent as if he were tripping and falling over
- his head is as big as his lower body
- his torso is almost nonexistent
- the arms are longer than the legs

This all sounds kinda harsh, but hey you asked ^^ and I'd really like you to try following  a reference with a wider canvas.

Hey ! If I were you, I'd let go of the 16x16 pixels constraint for now. It's really difficult representing something that's anatomically correct and recognisable at such a small scale, and what I consistently see with your sprites is that they seem "crushed" in their tiny space.
Widen your canvas size a bit, it'll give you more room for creating, experimenting and learning imo. Then when you're more experienced and comfortable with the art of placing pixels, you can move on to a smaller canvas and add constraints such as color count, etc.

Pixel art is hard enough to get comfortable with without adding even more difficulties ^^

Your animation is quite brutal/violent ! Especially for an idle animation which is supposed to be quite subtle, here the tail is fine but the head and ears twitch too violently, it almost looks like your cat is having a seizure xD
You should look into subpixel animation, which is a slightly more complex aspect of animation, but following that tutorial could help with your idle here