To obtain this achievement you need to play 10 Arena matches. Unfortunately unless you have friends that play this game, it is unlikely you will obtain this naturally as the game mode isnt played due to the fact that it is really no different than a casual match.
Simple way to achieve this on your own is to have a dummy account or perhaps a family members account. Set it up to have the Family sharing.
IMPORTANT* You can not launch a game with the Dummy account while the account owner is playing any game. Have the main account just sitting at the steam menu.
Launch the game with the Dummy account and load an online game and ready up for an arena match.
Now launch the game for the main account. This will give the other account a 5 min warning that they will be booted off. That is just enough time to get into the lobby and enter the arena and fight the dummy account. You should be able to finish with 1 minute left.
After the battle is complete. Quit the game completely as the main account. This will stop the timer on the Dummy account getting kicked out. You can then relaunch and repeat, quitting after every match.
It is a bit cumbersome but you gotta do what you gotta do.