This challenge is fairly easy with one card: Craterhoof Behemoth. This is a free card with a recent update.
Make a token deck featuring the green color. You might want to sprinkle in white (I used a black/green deck). Add cards like Jade Mage, Mycoloth, Selesnya Evangel, Raise the Alarm, Triplicate Spirits, Doubling Season, and other cards that generate 1/1 creature tokens. Then, when you have 32 creatures ready to attack you can drop Craterhoof Behemoth and chaaaarge! This will deal at least 1000 damage.
You can get this in any mode, but you can also play against a dummy deck in a practice match to let you build up your forces (instructions for doing this are available in solutions for other achievements in this game). Sorry didn't have a lot of time to write this solution, but if you have any questions or think I need to add something please let me know! Cheers!
Edit: I should also point out this should be cumulative. You don't need to get 1000 damage in one match or anything. It can be strung out over several matches.