The fastest way to get this achievement is to made a lockpicker (you dont need a premium account to lockpick, it will just be more hard than usual), and head to Sarducaa. That continent its really full of chests, you will find chests pretty everywere and the ones named only "chest" are the easiest one of the entire game: just two pins, easy and fast to open.
If you need lockpicks you can buy them at Beth Jedda, the smuggler who sell this item it's hidden in a roof close to where you can find stables and the priest. To reach him you need to use the city wall and jump in the roof.
If you need fast money to buy some lockpick you can easily farm the monsters called "Ratzar Worker" and sell the antennas for 1 gold each. You can find Ratzars all around Beth Jedda.