This achievement may be difficult since for some, since most barrel cards aren't available at the start of the game. But if you have a barrel of barrels, this achievement would be simple. Since you already play the barrel, and you get another. There's lots of barrel cards in the game but if you are looking to complete this achievement as quickly as possible, cheap barrels like Toxic Waste Imp, Genetic Experiment and Barrel of Barrels.
The best hero to use to achieve this is Impfinity, as he has access to Barrel of Barrels, Loose Cannon, Barrel of Deadbeards, Buried Treasure, Toxic Waste Imp and Barrel Roller Zombie. Nearly every card he has access to is very cheap and easy to play quickly, which makes completing this achievement very fast. Neptuna also has access to more barrels too (Zombot Battlecruiser 5000, Genetic Experiment and Trash Can Zombie), but it is recommended to use Impfinity since he has cheaper and easier to obtain Barrel Cards.