To start go into Campaign on the main menu, original Campaign and then select New Game +. Select a save slot which will create a lobby.
Select an Act to play, making sure to start in the 1st chapter of your selected Act.
Go to New Game + Settings, go to Customization and switch the option for Marcus As Batista Override to On. If you also put weapon skins to use Multiplayer skins as on, you can pick up the achievements for 10x kills and a chapter complete with a Custom skin, just make sure you’ve set up your MP weapon skins 1st.
Change the difficulty to beginner for a quicker run if you want and then hit Start.
Run through the whole Act as normal with the Marcus character and voice change and that will net you the achievement. You don’t have to play as Marcus, you don’t even have the option.
P.S. My achievements didn’t pop straight away, I had to shut the game down and when it loaded back in, it slowly popped on the main menu screen.
Good Luck with the Achievement.