wp-docs

Edit the file called “YourWordPressFolder/wp-admin/edit-link-categories.php”

Look for the code below (should start around line 76)
$pagenum = absint( $_GET['pagenum'] );
if ( empty($pagenum) )
$pagenum = 1;
if( !$catsperpage || $catsperpage < 0 )
$catsperpage = 20;
Change $catsperpage from the last row to whatever you wish.

The default value for $catsperpage is 20.