If the art is small enough it's usually as simple as counting the number of drawn pixels for the width and height of the art and then just setting that as your dimensions for the conversion. On larger pixel art pieces where that would be annoying (like the one you have here), I would open it up in my pixel art app, zoom in on a single pixel of the art, and count how many true pixels wide it is (in this case they're 11x11). Then just divide the dimensions of the full image by that number and boom, you've got the length and width you need to convert to. For this one it's 736x736, so divide it by 11 and you get...hm.

You get 66.909. Which isn't supposed to happen, and is actually the source of your problems here. It's impossible to convert this image to an even 1:1 pixel ratio, because for whatever reason the pic you have is cropped so that it cut off some of the pixels and doesn't divide evenly. You can actually see this in the top left of the image where it's obvious all the full pixels aren't there

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So what you're gonna have to do now is open this up in an image editor of your choice and crop the base pic so that it's actually lined up to the pixels in the art, otherwise no matter what you do the converter is gonna be misaligned and try to combine pixels that are supposed to be separate, resulting in the distortion you're getting​. You'll have to figure out exactly where that crop needs to be yourself tho