There are many special achievements in "Silent Hill 2: Remastered (SILENT HILL 2)", and muting the radio is one of them. The requirement to achieve this achievement is to complete the game without using the radio, but the radio is turned on at the beginning. Yes, you need to turn it off first.
How to achieve Silent Hill 2 Radio Silence achievement
Mute the radio
Complete the game without using the radio.
The radio is in the house north of Martin Street and must be picked up to trigger the first enemy battle. Unfortunately, it is on by default and must be turned off manually via inventory. Close it immediately after picking it up and keep it closed until the game is over.