Recently one of my colleagues brought into my attention that list attachments were not getting indexed and hence not showing in search results. We did some research and tests together and it is found that attachments are actually getting indexed and can be searched! I’ve seen a lot of people asking the same question in various blogs. I guess the confusion arouse because of the way SharePoint shows the search result for attachment. In the search results, SharePoint doesn’t really provide a direct link to the attachment. Instead, it displays link to the list item containing the attachment. But in the description of the search result, you can see the words from the attachment that you searched for. This is a bit disappointing because the search result would be confusing and useless if the list item has multiple attachments. The user won’t know which attachment contains the words he searched for.
Saji Viswam's Blog 
Hi how can get that attachments in a search result page i am able to get that custom column values by creating the managed properties and mapping to crawled property but how can i map the attachment filed and how to get that one
Solution for the attachment Link in the SharePoint search is available in the below Link.
http://sharepointsnacks.blogspot.in/2014/02/list-attachment-link-in-sharepoint-2013.html