The Sinking City 2 has two primary collectibles that you can find throughout the game. One is the Emergency Relief Crates, which give you items and upgrades. The second one is the Mushroom Jack Broadcasts, which you don't actually collect. Instead, you "collect" the broadcasts by listening to them for the additional lore information they give you.
The point of collecting these broadcasts is to get the Mycophile achievement. If you don't care about the extra story information from the broadcasts, then you don't have to actually listen to them in full in order to get the achievement. You just have to interact with the radio and get the broadcast to start, and it's considered collected at that point. It's important to note that you need to listen to all the broadcasts in one playthrough to get the achievement.
The apartment building has the first broadcast, and there's only one that you need to find in this section, as the next one won't be until you reach the church. For this broadcast, you'll get the achievement for tuning into your first Mushroom Jack show.
You'll find this radio in the room across from the room at the entrance where you pick up the map. However, you have to open the safe in Apartment 5 first, because the room with the radio is only unlocked after that point in the game.
For the church, you have to get the Church Key and enter the chapel building on this section of dry land. The back of the chapel has a safe room, then there's a ladder that takes you to the loft, which is where you use the Star Key when you have it. The radio is set up right outside the door. You go past this radio at least twice for the main quests, so make sure you interact with it during one of those times.
The broadcast at the bar is easy to grab, but it's also easy to miss. It's sitting on the bar, but you have to be behind the bar to reach it. So, go around to the corner of the bar, through the room there, and you pop out behind the bar, able to collect the broadcast.
After the bar, you get a bit of a break from finding broadcasts, as the next one won't be until you move the whale and get into the hotel. The radio here is on the counter at reception, which is where you pick up the map and right next to the safe room, so you'll be running past it quite frequently.
This is the first location that has multiple broadcasts to find. There are a total of three radios in the hospital with Mushroom Jack broadcasts on them.
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