This achievement is very straight forward. You just need to inflict 20 points of damage on your opponent in one turn. It can be direct damage, Trample damage, etc.
This can be done in any mode, whether it be Two-Headed Giant, Campaign or Multiplayer.
I think the simplest way to do this is to use the prebuilt green deck and wait until you get enough Green Mana to play Duskdale Wurm. On your next turn, play Blanchwood Armour on it, which will give it at least 14/14. If you have Overrun, play that next turn, and you've got a 17/17 monster with Trample. Then, just tap everything and play all your attacks.
A full list of the decks within the game can be found here.