To access this game mode you will have to go to the main menu of the game and look for the option "Battlemode" and select it, the game will recommend you to play during the campaign up to a certain point before entering the mode. You can go back and complete what is necessary in the campaign or just go ahead in multiplayer.
Which will take you to the main menu of the mode, where you will be given instructions on this and when finished you can start playing it taking into account that it will be necessary to have all the updates and the account active according to your game platform.
Now that you know how to play Battlemode in Doom Eternal you should be more than ready to play this game mode, remember that for you we have a lot of content about this game and a lot of other titles that you will surely want to review.
PlayStation 4 PS4, Xbox One, Microsoft Windows PC, Nintendo Switch, Stadia