The below steps can be followed for enabling diagnostics at user level.

1. Navigate to System Administrator responsibility> Profile> System>

 
 
2. Enter profile name: Utilities:Diagnostics .
    Enter Application User for whom you want to enable Diagnostics.
 
 
Enter value Yes at User level and Save the Changes . You can set yes at site level for all application users.

 
3. Navigate to System Administrator responsibility> Profile> System>
Enter profile name: Hide Diagnostics menu entry.
Enter Application User for whom you do not want to hide Diagnostics menu entry .
Enter value No at User level and Save the Changes .
  

 
 
 
4. Logout from Oracle Application and login again.Diagnostic would be enabled.