This has come up before but I don't have enough reputation to comment into the original questions.
User webchun gave a great tutorial in How to show tagged items in category blog layout which works really well, but he wrote it referencing Joomla 3.4.4 and the templates have changed in the new releases.
Using his method, I got a much nicer blog layout, but each item is displaying twice. Has anyone else had any luck developing this further?