<p>As far as I know, almost all the badges are still earnable.  The rare exceptions are <a href="https://stats.stackexchange.com/help/badges/67/precognitive">Precognitive</a>, <a href="https://stats.stackexchange.com/help/badges/30/beta">Beta</a>, and <a href="https://stats.stackexchange.com/help/badges/88/analytical">Analytical</a>.  That is, the <a href="https://stats.stackexchange.com/help/badges/51/unsung-hero">Unsung Hero</a> badge can still be earned.  </p>

<p>However, not all badges are trackable from your profile page.  As @whuber notes, these issues are covered on <a href="https://meta.stackexchange.com/">meta.SE</a>.  You can find a list of badges that cannot be tracked in this thread: <a href="https://meta.stackexchange.com/q/263610/187282">Why aren't all the badges shown on the track menu?</a></p>
