As the achievement states, this is at the very end of the game. You will engage in a dialogue with Letho, who will offer a toast to the end of their grievances. After there will be another choice in the dialogue to either fight Letho or to let him walk away. For this achievement (you will absolutely want to do this on Dark), you will need to spare him and let him walk away.
For "Avenger", you will need to kill him. I'd suggest doing this on easy, just because the fight is incredibly difficult on Dark, but it's identical to what it is in Chapter I.