Tropical Jungle - Digimon World 1
Normally the Tropical Jungle will be the second or third area that you explore in the game. You can reach this area by recruiting Coelamon in the Native Forest. Our first time talking to Coelamon will get you access to the Tropical Jungle and repair the Digimon Bridge connecting it to File City.
There are a total of four Digimon to recruit here but you will only be able to get two of them early on. Both Betamon and Centarumon are the important ones for you to get early.
Betamon (Mangrove Region)
Requirement: N/A
Betamon is the easiest Digimon to find in the Tropical Jungle and easiest to recruit. When you enter this area from the Digimon Bridge go east until you hit another bridge that leads to the area with a lot of vines/trees. This is known as the Mangrove Region and there are two exits you can take here. One will lead you to Betamon and the other to Centarumon. You'll find Betamon in the top right of the Mangrove Region and he will join you without a fight when you talk with him.
Centarumon (Amida Forest)
Requirement: N/A
You'll find Centarumon in a unique area called the Amida Forest, it can be accessed by going through the Mangrove Region which is found in the eastern portion of the Tropical Jungle. Just like reaching Betamon, you'll want to enter the Tropical Jungle from Digimon Bridge and run east along the beach until you cross another bridge and the terrain changes to many vines and trees. Keep going east into a new region from here and then go north.
On the way to Amida Forest you'll pass a sign warning you that trespassers will be shot. Kind of like the signs you see in rural areas! Unlocking Centarumon can be a bit annoying because the puzzle to reach him isn't very clear. This is called a Ghost Leg Puzzle and to solve it you need to turn at every opportunity when running up the gauntlet.
My advice is to start with the left hallway and zig zag up until you reach the top. Pause momentarily in the middle path to see what door has an O on it (this is the door we need). If you get blown away from the door with an O it means you need to backtrack a bit and turn before you run up the straight route. Here is a Youtube Video that demonstrates what I mean.
Vegiemon
Requirement: Recruit Palmon into the city
Aside from recruiting Palmon, you'll also need to wait until the 15th day of the year to get the Rain Plant (pictured above) in File City. When you open your inventory window (Triangle by default) you will see the day and the year at the top. Once you have the Rain Plant, you can get Vegiemon at any time in the future.
The location of Vegiemon is one screen east of the toilet in the Tropical Jungle. In this area you'll find a small seedling (pictured below) which asks you to use an item on it. The item you need to use is the Rain Plant, this will spawn Vegiemon and he will join your city.
Use the Rain Plant on this seedling in the jungle
Piximon
Requirement: N/A
Enter Tropical Jungle from the Digimon Bridge and travel east along the beach, the first screen to the east is where Piximon can spawn. He has a ~5% or so chance of spawning each time you enter the screen so you'll pretty much be exiting and entering over and over again to spawn him.
Piximon is an ultimate Digimon so you should expect a difficult fight from him.