This is SP2010. Is there a way to allow managers to edit a user's profile as seen in their My Site profile?
It is little complicated, how many managers you want to give this kind of permission? If one then it really easy, otherwise create a group and add all managers in it then delegate them Manage Profile Permissions.
To delegate administration of User Profile service features by using Central Administration
- Verify that the user account that completes this procedure has the following credentials:
The user account that performs this procedure is a member of the Farm Administrators SharePoint group or has been delegated permission to administer the User Profile service application that is running in the farm.
Start SharePoint 2013 Central Administration.
For Windows Server 2008 R2: Click Start, click Microsoft SharePoint 2013 Products, and then click SharePoint 2013 Central Administration.
For Windows Server 2012:
On the Start screen, click SharePoint 2013 Central Administration. If SharePoint 2013 Central Administration is not on the Start screen: Right-click Computer, click All apps, and then click SharePoint 2013 Central Administration.
In Central Administration, in the Application Management section, click Manage service applications.
In the list of service applications, click User Profile Service Application.
On the Service Applications tab, in the Operations group, click Administrators.
On the Administrators for User Profile Service Application page, type or select a user or group account, and then click Add.
In the Permissions for User /Group: box, check the feature or features for which you want to delegate Manage Profile, and then click OK.
Alos Check this one