With the release of an updated Grand Theft Auto III for the PS4 on December 5th, 2015 came trophy support. There are 29 trophies.
King of Liberty City - Platinum
Unlock all trophies
First Day on the Job - Bronze
Complete "Luigi's Girls"
Hunting Season - Bronze
Destroy five helicopters
Disposing of the Evidence - Bronze
Crush a car at the junkyard
Repeat Offender - Bronze
Get busted 20 times
Street Sweeper - Bronze
Waste 100 gang members
iGrandTheftAuto
Population Control - Silver
Waste 1,000 people
If You Ain't Cheatin', You Ain't Tryin' - Bronze
Blow up 2,000 cars
By a Mile - Bronze
Complete the "Turismo" race in under 180 seconds
Wreckless Driving - Bronze
Perform a perfect insane stunt
Wheels Up - Silver
Complete 20 unique jumps
Where we're going, we don't need roads - Silver
Complete "Patriot Playground", "A Ride in the Park", "Multi-Story Mayhem", and "Gripped!" missions
Where To? - Silver
Complete 100 taxi fares
Blood in the Streets - Silver
Pass all 20 Rampages
Play Fetch - Gold
Complete the Portland Docks and Shoreside Vale import/export car lists
Pest Control - Silver
Deliver all emergency vehicles to the crane at the Portland Docks
A Marked Man - Silver
Complete "Last Requests"
iGrandTheftAuto
Offshore Delivery - Silver
Complete "A Drop in the Ocean"
Not So Fast - Gold
Complete "The Exchange"
A Gift from the King - Silver
Complete the "Kingdom Come" mission
Man Toyz - Silver
Complete every RC Toyz mission
Splish Splash - Bronze
Extinguish 20 fires during a single Fire Truck mission
Playing Doctor - Silver
Complete Paramedic level 12
Going Rogue - Bronze
Kill 20 criminals during one Vigilante mission
Dirty Money - Bronze
Amass a fortune of $1,000,000
Right-hand Man - Silver
Earn a criminal rating of 2,500
Like a Boss - Gold
Earn a criminal rating of 5,000 or higher
Liberty City Secrets - Gold
Collect 100 hidden packages
Is That All You've Got? - Gold
Achieve 100% completion