Before you start a new game click on Options at the main menu and toggle both Classic Commentary and Updated Commentary to On. If you don't turn these on before you start a new game you won't unlock the achievement as the first commentary will happen as soon as you exit the Options screen.
When the credits start at the end of the game you can hit escape to blow past them and see a final scene. After that you get the final commentary and the achievement will pop.
As you are playing you can hit the space bar to dismiss the commentary as soon as it pops up. You don't have to listen to any of it if you don't want to.