code the form to collect all of the checkboxes into an array using the primary key field of the table:
record 1 <input type="checkbox" name="archive[]" value="1"><br>
record 2 <input type="checkbox" name="archive[]" value="2"><br>
record 3 <input type="checkbox" name="archive[]" value="3"><br>
etc...
then on the form processor do a query like this:
$result = mysql_query("UPDATE table SET archive = 'Y' WHERE id IN(" . implode(',', $_POST['archive']) . ")");
i'm assuming you are using mySQL. if you are, be advised that mySQL does have a boolean field type but it is very common to simply use a CHAR(1) field that defaults to NULL (NULL = false, Y = true). this will save storage over using the strings "YES" and "NO".