This page of the trophy guide to Death Stranding has a detailed description of Public Service Porter trophy. This bronze trophy is received for disposing of chiralium-contaminated cargo by throwing him into the crater lake.
In order to get this trophy, you must visit the Junk Dealer. The Junk Dealer is located in the central region. You can start, for example, in the Distribution Center South of Lake Knot City and head south-east.
When you get there, look for chiralium-contaminated cargo lying near the building with the terminal. Take only one of them. You don't need to carry it in your hands, you can put it on the hero's back.
Crater lake is located a few hundred meters south of the Junk Dealer. You can get there on foot or in a vehicle.
Once you reach your destination, stop at the shore.
Select the chiralium-contaminated cargo and place it in Sam's hand.
While holding the cargo (hold the L2 and R2 buttons), press the Square throw the container. It must fall into the water and drown. After a while, you should get the trophy.