Turn the string into a jQuery collection by passing it to $, and then you can get the text of the Attachments node with .find('Attachments').text():
const htmlStr = '<?xml version="1.0" encoding="utf-8"?><FormVariables><Version /><Attachments type="System.String">example_image_1_portrait_HD.jpg</Attachments></FormVariables>';
console.log($(htmlStr).find('Attachments').text());
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
But note that there's no need at all to depend on a big library like jQuery just for XML parsing - you can achieve this using the built-in DOMParser instead:
const htmlStr = '<?xml version="1.0" encoding="utf-8"?><FormVariables><Version /><Attachments type="System.String">example_image_1_portrait_HD.jpg</Attachments></FormVariables>';
const doc = new DOMParser().parseFromString(htmlStr, 'text/html');
console.log(doc.querySelector('Attachments').textContent);