I think you done a good job, but here are a few things I'd suggest you to fix to make this icon get recommended or highly recommended grade.
Cross guards blends with background too much. Try to find different hue for it or burn it more at least. The light on blade should go in one direction only (if you want to dodge light in vertical angle than make it only in that direction, same goes for horizontal option). Strokes in too many random directions make blade look too shiny and as if it was made from shiny stone, not metal (or silver, it doesn't really matter what material you prefer as long as it is apparent). Also I'd suggest sizing down the brush size a bit.
Sword false edges are not symmetrical and the point should be far more sharper. You could try to more whole image to left to have less unused space between icon frame and sword tip. Have it on mind that light reflection lines on left false edge are supposed to be the brightest part of image. Also there should be more definition between the meeting place of blade and guard. There is no prominent details which I'd strongly recommend you to add, especially on guard, grip and fuller line (depressed line in the middle of blades).
Proper shading is quite important for overall look of sword, so define a light source position correctly. Basically, focus on blade's shade and the accompanying sword details, and again, reduce the brush size if adding them. Not sure what program you used to make it, but in gimp (that I use for my icons) there are filters for sharpening and blurring so mix them with hue altering to get flow between background and sword. Ofc, try not to repeat colors from blade on background.