Please apply the phpld deeplinks mod before adding this feature.

This will give you the ability to show and edit the additional fields in the admin panel. 3 Files will be edited so I recommend that you back them up before applying the modifications.
Files to edit:
admin/dir_approve_links.php,
templates/Core/admin/link_details.tpl,
templates/Core/admin/dir_links_edit.tpl.

First in admin/dir_approve_links.php
FIND:

$columns = array ('TITLE' => _L('Title'),
'URL' => _L('URL'),
'DESCRIPTION' => _L('Description'),
'CATEGORY' => _L('Category'),
'RECPR_URL' => _L('Recpr. Link URL'),
'PAGERANK' => _L('Pagerank'),
'DATE_ADDED' => _L('Date Added'));

REPLACE BY:

$columns = array ('TITLE' => _L('Title') ,
'URL' => _L('URL'), 'TITLE1' => _L('Title1'),
'URL1' => _L('URL1') , 'TITLE2' => _L('Title2'),
'URL2' => _L('URL2') , 'TITLE3' => _L('Title3'),
'URL3' => _L('URL3') , 'TITLE4' => _L('Title4'),
'URL4' => _L('URL4') , 'TITLE5' => _L('Title5'),
'URL5' => _L('URL5'),
'DESCRIPTION' => _L('Description'),
'CATEGORY' => _L('Category'),
'RECPR_URL' => _L('Recpr. Link URL'),
'PAGERANK' => _L('Pagerank'),
'DATE_ADDED' => _L('Date Added'));

Second, in templates/admin/link_details.tpl
FIND:

<tr class="{cycle values="odd,even"}">
<td class="label">URL:</td>
<td class="smallDesc">{$linkInfo.URL|escape|trim}
</td>
</tr>

BELOW it, ADD:

<tr class="{cycle values="odd,even"}">
<td class="label">Title1:</td>
<td class="smallDesc">{$linkInfo.TITLE1|escape|trim}
</td>
</tr>

<tr class="{cycle values="odd,even"}">
<td class="label">URL1:</td>
<td class="smallDesc">{$linkInfo.URL1|escape|trim}
</td>
</tr>

<tr class="{cycle values="odd,even"}">
<td class="label">Title2:</td>
<td class="smallDesc">{$linkInfo.TITLE2|escape|trim}
</td>
</tr>

<tr class="{cycle values="odd,even"}">
<td class="label">URL2:</td>
<td class="smallDesc">{$linkInfo.URL2|escape|trim}
</td>
</tr>

<tr class="{cycle values="odd,even"}">
<td class="label">Title3:</td>
<td class="smallDesc">{$linkInfo.TITLE3|escape|trim}
</td>
</tr>

<tr class="{cycle values="odd,even"}">
<td class="label">URL3:</td>
<td class="smallDesc">{$linkInfo.URL3|escape|trim}
</td>
</tr>

<tr class="{cycle values="odd,even"}">
<td class="label">Title4:</td>
<td class="smallDesc">{$linkInfo.TITLE4|escape|trim}
</td>
</tr>

<tr class="{cycle values="odd,even"}">
<td class="label">URL4:</td>
<td class="smallDesc">{$linkInfo.URL4|escape|trim}
</td>
</tr>

<tr class="{cycle values="odd,even"}">
<td class="label">Title5:</td>
<td class="smallDesc">{$linkInfo.TITLE5|escape|trim}
</td>
</tr>

<tr class="{cycle values="odd,even"}">
<td class="label">URL5:</td>
<td class="smallDesc">{$linkInfo.URL5|escape|trim}
</td>
</tr>

FINALLY in templates/admin/dir_links_edit.tpl
FIND

<tr>
<td class="label required">
<label for="URL">URL:</label></td>
<td class="smallDesc">
<input type="text" id="URL" name="URL"
 value="{$URL|escape|trim}" class="text"/>
{validate form="dir_links_edit" id="v_URL"
 message=$smarty.capture.invalid_url}
{validate form="dir_links_edit" id="v_URL_U"
 message=$smarty.capture.url_not_unique}
</td>
</tr>

BELOW it , ADD

<tr>
<td class="label"><label for="TITLE1">
Title1:</label></td>
<td class="smallDesc">
<input type="text" id="TITLE1" name="TITLE1"
 value="{$TITLE1|escape|trim}" class="text" />           
</td>
</tr>
<tr>
<td class="label"><label for="URL1">
URL1:</label></td>
<td class="smallDesc">
<input type="text" id="URL1" name="URL1"
 value="{$URL1|escape|trim}" class="text"/>
</td>
</tr>
      
<tr>
<td class="label"><label for="TITLE2">
Title2:</label></td>
<td class="smallDesc">
<input type="text" id="TITLE2" name="TITLE2"
 value="{$TITLE2|escape|trim}" class="text" />           
</td>
</tr>
<tr>
<td class="label"><label for="URL2">
URL2:</label></td>
<td class="smallDesc">
<input type="text" id="URL2" name="URL2"
 value="{$URL2|escape|trim}" class="text"/>
</td>
</tr>
      
<tr>
<td class="label"><label for="TITLE3">
Title3:</label></td>
<td class="smallDesc">
<input type="text" id="TITLE3" name="TITLE3"
 value="{$TITLE3|escape|trim}" class="text" />           
</td>
</tr>
<tr>
<td class="label"><label for="URL">
URL3:</label></td>
<td class="smallDesc">
<input type="text" id="URL3" name="URL3"
 value="{$URL3|escape|trim}" class="text"/>
</td>
</tr>
      
<tr>
<td class="label"><label for="TITLE4">
Title4:</label></td>
<td class="smallDesc">
<input type="text" id="TITLE4" name="TITLE4"
 value="{$TITLE4|escape|trim}" class="text" />           
</td>
</tr>
<tr>
<td class="label"><label for="URL4">
URL4:</label></td>
<td class="smallDesc">
<input type="text" id="URL4" name="URL4"
 value="{$URL4|escape|trim}" class="text"/>
</td>
</tr>
      
<tr>
<td class="label"><label for="TITLE5">
Title5:</label></td>
<td class="smallDesc">
<input type="text" id="TITLE5" name="TITLE5"
 value="{$TITLE5|escape|trim}" class="text" />           
</td>
</tr>
<tr>
<td class="label"><label for="URL5">
URL5:</label></td>
<td class="smallDesc">
<input type="text" id="URL5" name="URL5"
 value="{$URL5|escape|trim}" class="text"/>
</td>
</tr>

The second step will show the additional fields when hovering over the link title in admin panel when approving links or viewing links.

The third step will show them when editing the listing in the admin panel.

Many thanks to Bobby from the forums of phpld for all the help he gives to the members there.