This trophy is a little tricky. Basically you need to have complete the Campaign, the Challenges, and unlocked all the cards for each deck. Each time you win a game of any type in Single Player or Multiplayer, you will unlock a card for the deck you're currently using. Certain decks are unlocked upon completing the Single Player Campaign. You can press in the main menu to see a list of decks you've unlocked, number of cards unlocked for each deck, as well as change decks and/or customize them to a very limited extent.
Now here comes the tricky part, at the bottom of main menu you will see a % counter that indicates your total unlock progress. The problem is, this counter tracks your overall unlock progress of the Core Game AND DLC if you have it. If you had 90% in the Core Game and decided to install all 3 DLC, your unlock progress tracker will drop to somewhere about 40%. So if you have installed DLC, you obviously have much more to do by completing more campaigns, challenges and even more Decks to unlock and complete.
My advice is to complete 100% of the Core Game before installing any DLC if you want to save ALOT of time.
Note: I can confirm that you can delete the game if you have DLC installed, reinstall the Core Game only then work on this trophy. Don't worry your save file will still contain your DLC progress. As soon as the counter hits 100% the trophy will unlock. Sometimes the game will round up your progress from 90+ % to 100% even if you have not unlocked everything. I had one more deck to complete when the trophy unlocked. You can then re-download your DLCs from PSN store and work on the expansions if you like.
One method of boosting this is to create an online match and trade wins with another player by having one side concede the game upon starting. The winner will continue to unlock cards for the deck he is using, but first he should make sure he has unlocked all the decks via Single Player Campaign.