Made some tweaks as follows:  
November 13, 2018:

 - Fixed the icon cutoffs.
 - Streamlined the `@exclude`s.

November 16, 2018:

 - Switched to proper SE image host because svgshare.com was crashing and "exceeding quota".
 - Restored scripts to review paths, since they need duckies too.
 - Moved the script to GitHub, where we can support it more effectively.

Feel free to incorporate any of this into the question post, if you wish.

### Source:
See [Stack Exchange, replace badge icons with duckies... on GitHub][1] and **post bug reports and pull requests there.**

#<kbd>[Install from GitHub][2]</kbd>


----------
Version 2 reference (See GitHub for any future versions):

    // ==UserScript==
    // @name        Stack Exchange, replace badge icons with duckies
    // @description Does what it says on the tin.
    // @match       *://*.askubuntu.com/*
    // @match       *://*.mathoverflow.net/*
    // @match       *://*.serverfault.com/*
    // @match       *://*.stackapps.com/*
    // @match       *://*.stackexchange.com/*
    // @match       *://*.stackoverflow.com/*
    // @match       *://*.superuser.com/*
    // @exclude     *://api.stackexchange.com/*
    // @exclude     *://blog.*.com/*
    // @exclude     *://chat.*.com/*
    // @exclude     *://data.stackexchange.com/*
    // @exclude     *://elections.stackexchange.com/*
    // @exclude     *://openid.stackexchange.com/*
    // @exclude     *://stackexchange.com/*
    // @grant       GM_addStyle
    // @run-at      document-start
    // @version     2.0
    // @history     2.0 Switch to SE image server for more reliable hosting.
    // @history     2.0 Placed script in GitHub. Review gets duckies too.
    // @history     1.5 Fix icon cutoff problem that many sites had.
    // @history     1.0 Initial release
    // @author      Samcarter
    // @homepage    https://stackapps.com/q/8116/7653
    // ==/UserScript==

    GM_addStyle ( `
        /* change icons of badges */
        .badge1, .badge2, .badge3 {
            background-image: url("https://i.sstatic.net/zm5Pg.png") !important;
            margin: 0 !important;
            width: 14px !important;
            height: 14px !important;
        }
        .badge1 { background-position: -39px 1px !important; } /* Gold */
        .badge2 { background-position: -19px 1px !important; } /* Silver */
        .badge3 { background-position:   1px 1px !important; } /* Bronze */
    ` );


  [1]: https://github.com/BrockA/SE-misc/blob/master/Stack%20Exchange,%20replace%20badge%20icons%20with%20duckies.user.js
  [2]: https://github.com/BrockA/SE-misc/raw/master/Stack%20Exchange%2C%20replace%20badge%20icons%20with%20duckies.user.js