<-- palette + lighting edit
<-- lighting only edit
(NOTE: I only modified the lighting on the chest/shoulder areas and some very slight modifications to the head and back portions of the silhouette's animation)
(I also tweaked the shines on your legs and your little tassel animation on the helmet for fun. ;P)
For the most part, you're doing a fairly decent job. The main issue is that your lighting is a bit extreme on the turns to the left/right for no apparent reason and this makes adding contrast very difficult due to only having a limited number of shades to work with. Even with ultra-shiny metal, there are still shadows and planes that must be accounted for.
With that said, your only other problem is that the palette lacks interesting colors and contrast. With my edit of your palette, I darkened the yellow next to the white, and went just past red, stopping just short of a purple hue at a rust red, with some of the shadows (making them more of a rusty red than a red-brown emphasizes the gold 'tint' on the metal when saturation is added and the rust color is darkened.)
There are many more additional improvements that can be made over the rest of the sprite, but my edits were meant to show you the main problems with your coloring/lighting by using the chest and shoulder area of the animation as an example of how to do the lighting of the forms more clearly. And although I understand the appeal in adding a lot of light/shadows to your turning in 3d, do this only when there is extreme movement into the third dimension (such as on the sword) because the number of palette entries (not to mention the amount of effort) will increase exponentially the more levels of depth you add to your sprite's coloring.
It's usually best to simply fake fancy 3d color depth like this by using extra palette entries only for certain limbs/attachments, and implement the forms with 3d planes and heavy contrast in your lighting (such as on the chest/shoulder areas of my edit) in order to keep from increasing the number of colors too much (which is why I didn't edit the entire animation -- too much work keeping up with all those similar color values). If you look closely at my chest and shoulder animation, I used 4-5 colors to indicate the 3d-form of the distance between both shoulders across the entire animation.
Since the additional color entries were there, I also tweaked them with a little more red to separate them from the yellow, to give the metal a bit more of a metallic feel, but please note that I spent zero time working on the forms and lighting after tweaking these entries, so they look slightly odd across the animation in certain places -- I meant only to show you ways to make the palette more interesting and let you play with that new palette to practice tweaking the additional forms/lighting in the animation.