Fairly simple trophy: once you unlock the "City" area, you can go there and see a spinning column with little white dots all over it. ADA will tell you that spinning column needs to go down.
Immediately leave the area and head for TOWN.2 (where your first SOS mission took place). You will see little purple orbs floating around - take these out and you will unlock the SNIPER sub-weapon, and have 20 shots available.
Head back to the CITY and REMAIN STATIONARY WHERE YOU ENTERED THE LEVEL. Literally, do not move at all.
Switch to your SNIPER (up and down buttons on the directional pad) and get the white dots on the spinning column anywhere in your reticule. It does not have to be dead center, just close: the game will compensate severely even if you are off.
Destroy the column without initiating combat with any enemy and this trophy will pop.