Unmissable story achievement. Can be done on any difficulty.
Bane can be a tough fight. When he charges, hit him with a batarang, then dodge left or right. Sometimes he'll be fine, and sometimes he'll start rubbing his eyes. If he isn't rubbing his eyes, try again. When he is rubbing his eyes, run up and hit him three times. Repeat three or four times.
He'll spawn unarmed goons after each successful attack. I recommend dealing with them before going for another hit.
Roosterteeth's video shows how to get this and a few other achievements.