How can I animate this?

There is no magic answer to this question

Ask yourself what do you want your sprite doing. Walk ? Breath ? Dance ? Then draw something !

Aaaaw thank you Ryumaru, with such a piece, my crazy love for cats is fulfilled (^・ω・^ )
Nice GB palette, hehe

Merry Xmas to everyone !
Also, bravo for all these wonderful pieces of pixels 

Background is still too much repetitive. What about add some variations as for example : a hole in the wall, a window, a pillar, or some threatening vegetation running through the bricks ?  On the floor too : pots, bones, anything which could add deepness to your scene.

I am not sure of this, but I thing the overall piece seems a bit odd because there is no level-design/no real logic with the platform placement.

Well, it doesn't look like it was made "pixel by pixel" or more accurately, with a "pixel precision". It looks like more like a "classic" drawing (I mean, with mouse or pen, but with no intent to place pixels to form a specific shape), mixed resolution and use of symmetry doesn't help too. I'll pass on lack of shading as it is obvious there are bigger problems.

You should try simpler shape, and learn some basics about drawing