Achieving certain tasks will reward you trophies, which can be found on the Trophy Shelf in your apartment.

Trophy	How to unlock
Diamond Pillbox	Sell hallucinogens
Gold Medal	Get a score of at least 10,000 for a weapon.
Golden Binoculars	Discover 40 drug dealers
Jeweled Bong	Sell depressants
Jeweled Key To The City	Own all 21 safehouses.
Platinum Syringe	Purchase Heroine
Silver Safe	Make a $2000 profit
Titanium Briefcase	Discover all 80 drug dealers.
Wooden Spoon	Achieve a loss of $500