This basic GM script adds a "Pull requests only" tickbox to your dashboard issue pages on GitHub; clicking it hides non-PR issues. It doesn't work over pagination (without a refresh) or other things like that.

github.pr.tamper.js

// ==UserScript==
// @name          GitHub Assigned Issues Pull Requests tickbox
// @namespace     github-assigned-issues-pull-requests
// @version       1.0
// @description   Show only pull requests on the Assigned Issues dashboard page (e.g. https://github.com/dashboard/issues/assigned or the similar org page)
// @match         *://github.com/dashboard/issues/*
// @match         *://github.com/organizations/*/dashboard/issues/*
// @require       http://ajax.googleapis.com/ajax/libs/jquery/1.9.1/jquery.min.js
// @author        Matthew Somerville >> https://github.com/dracos
// ==/UserScript==

$('.issues-list-options').append('<div class="button-group"><label><input type="checkbox" id="pull_requests_only" value="1"> Pull requests only</label></div>');

$('#pull_requests_only').change(function(){
    var lis = $('.mini-icon-issue-opened').add('.mini-icon-issue-closed').closest('li'),
        count = $('.filter-item.selected span.count');

    if ($(this).prop("checked")) {
        lis.hide();
        var c = count.text();
        count.data('c', c);
        count.text(c-lis.length);
    } else {
        lis.show();
        count.text(count.data('c'));
    }

});