You unlock expansion cards by playing through the Garruk's Revenge campaign.
Main Menu -> Expansion -> The Hunt Begins
Once you have completed the first duel against Kento the Spiritcrafter, it will award you a booster pack. Open it, press
to access your deck manager.
(You can also access your deck manager from the main menu. Just pick a deck to edit from the ones you already have created.)
to set filters. Press "New Cards", as the newest cards you should have unlocked should be the ones you were just awarded. It will then arrange your cards from newest to oldest; press
to leave the filter panel. The selected card after leaving the filter panel should be a new card. Add it to your deck by pressing
. The achievement should pop upon doing so.
You can then exit out without saving your deck if you wish. The achievement does not require that you keep the card in your deck.