Trust you know that eSamudra works only on Internet Explorer, but perhaps their programmers made it specific to some particular version only! Error "For better performance you are advised to use Internet Explorer" have been found when trying to update esamudra profile with IE 11.
Possible solution is :
Recently when I did my GMDSS Renewal, I realised that I did not explain the use of compatibility mode of Internet Explorer. Like I said before DG Shipping profile will work with Internet Explorer version 7,8, 9 and 10. To know which version you are using
Click "Setting" >> "About Internet Explorer"
The popup opened will show you the version of your IE. To use the compatibility mode of IE (in simple terms making it to a lower version like IE 8 or IE 9)