There are plenty of locked chests scattered throughout the world so this one shouldn't be too difficult to grind out before the end of the game. To pick a lock you need to have a lockpick in your inventory and, 'gasp', a locked object.
Approach the object (typically a chest but doors count as well) and select it with X. From here you will enter the Lockpicking menu, which if you are familiar with games like this should come as no surprise and appear to be much easier than others. If you fail to pick the lock your lockpick will break and you can try again. Pick 50 locks successfully and this trophy is yours. Also note that using Prismere Lockpicks (a one shot item that automatically picks almost any lock) will count towards this trophy.
If you are really looking to finish this off as quickly as you can, you can head to the city of Rathir in the Plains of Erathell (it's the giant city appearing in the Northeast on your World Map). Enter the Common House and head West up the steps then into the Storeroom. Inside the room you will find roughly 15 locked chests to pick. Please note that some of these will be hard and very hard, but it is still a good place to finish grinding out this trophy.