Difference between 好累 and 很累
好 is more describing the feeling of your heart.


  我做了那麼多，都沒用。我好累。
  
  I did so much. But nothing is useful. I feel really tired. 


很 is just describing you're physically tired.


  我跑了10公里。我很累了。
  
  I've run for 10km. I'm very tired.


In most cases, 『好』 is more than 『很』. Just like the example above.