When sneaking behind an enemy, you can press Circle when you're close enough to pickpocket them (it takes multiple pickpockets to get a treasure). You can tell if enemies have a valuable treasure as their pouch will glow brightly, so don't bother with the measly amount of coins from enemies without.
You can pickpocket with every character except Carmelita. Murray can use the "Looty Shake" move buyable from Thiefnet to get treasures, which DOES count for the trophy. (Use Circle to pick the enemy up and press Circle again to shake them). So, if you chose, you can farm any infinitely respawning enemies for it during some jobs, but if you get hit while carrying them they get dropped and die, so it can be awkward to do.
There are 3 items per area, including from the Rat enemies in Paris. These can be obtained from any rats throughout the game, but you can keep restarting a checkpoint in the prologue if you want to get it out of the way early. As Bentley drops down into the sewers behind two guards, one of them normally has an item. Keep restarting till you get all three.
Full List:
Prologue:
1) Swiss Cheese - $100
2) Gas Grenade - $200
3) Tomato Juice Box - $500
Feudal Japan:
1) Kabuki Mask - $100
2) Mahjong Tile - $200
3) Ivory Chopsticks - $500
Old West:
1) Gold Nugget - $100
2) Deputy Badge - $200
3) Sliver Belt Buckle - $500
Ice Age:
1) Lava Rock Spearhead - $100
2) Amber Fossil - $200
3) Tribal Penguin Mask - $500
Medieval England:
1) Pocket Watch - $100
2) Platinum Gear - $200
3) Emerald Dragon Eye - $500
Arabia:
1) Pearl Earring - $100
2) Scorpion Tail - $200
3) Red Ruby Ring - $500
This will also earn you the "Oh Look It's Shiny" trophy when you collect 10 unique ones.