Hi,

Please check the Profile with the below permission:

Manage Dashboards

Also

Knowledge Article Number: 101725 

Description
I have Manage Dashboards" permission yet I cannot edit dashboards?

Resolution
Users with Manage Dashboards permission can create and clone however to edit dashboards that were not created by the user, the user must have View All Data permissions. This ensures that users without View All Data cannot create a dashboard with a Running User that would allow them a view of information beyond their access rights. Below is the breakdown of the permissions:
 
PERMISSION LEVEL 1
The "Manage Dashboards" profile permission allows a user to:
- Create a dashboard (in dashboard folders which they have access to)
- Clone an existing dashboard
- Edit dashboard YOU CREATED only (you cannot change Running User from yourself to anyone else)

In both cases, that user's username will be automatically set as the Running User and cannot be changed by that user to any other username.

NOTE: If a user sees the "Edit" button for a dashboard they didn't create they will still receive "Insufficient Privileges" message.

PERMISSION LEVEL 2
A profile ALSO needs "View All Data" permission to do the following:
- Edit a dashboard (including change Running User to anyone else) - exception above for editing your own dashboards minus Running User
- Set or change Running User
- Create or change dashboard folders and folder permission

NOTE: The Running User itself on a dashboard never controls anyone's access to that dashboard, only the data it returns when run.

Also go through the below links:

https://help.salesforce.com/apex/HTViewHelpDoc?id=faq_reports_control_access.htm&language=en_US

https://success.salesforce.com/answers?id=90630000000gwpRAAQ

https://success.salesforce.com/answers?id=90630000000go2nAAA

https://help.salesforce.com/HTViewHelpDoc?id=analytics_sharing_permissions.htm&language=en_US

https://help.salesforce.com/apex/HTViewHelpDoc?id=access_dashboard_folders.htm&language=en

https://success.salesforce.com/answers?id=90630000000ghw6AAA

Please do let me know if it helps you.

Regards,
Mahesh