How can I make the Twitter Tools plugin hyperlink every link?

Never used this plugin. WordPress has a function called make_clickable() which might help you.

Example:

$string = "This is a long text that contains some links like http://www.wordpress.org and http://www.wordpress.com .";
echo make_clickable($string); 

Output:

This is a long text that contains some links like <a href="http://www.wordpress.org" rel="nofollow">http://www.wordpress.org</a> and <a href="http://www.wordpress.com" rel="nofollow">http://www.wordpress.com</a> .