Age of Empires II: Definitive Edition

This one should be a gimmie if you play the scenario - he'll probably die to the Saxons/Avars/Lombards within about a half hour or so while you do absolutely nothing, so just start the game and boom and you'll be fine. You don't even need to complete the mission for it to unlock; it'll happen instantly so if you wanted to you could quit right there (but you wouldn't do that since a different achievement is for completing all of them).

If you're playing on Standard, the enemy AI might not be as aggressive but you can kite some Lombard/Umayyad/Avar forces to Carloman's base instead and you'd still be fine.

Or just kill him yourself I assume; you can't win the mission until he dies and it does say you can attack him you just won't take control of his base if you do.