The is the largest and most complex region in the game and we'll be covering it two parts, first the large pond to the south and west, then the ruins to the northeast.
Smokey Progg[edit]
This is an optional boss that's meant to be a challenge for skilled players. In fact it doesn't even appear after day 15 so you have to get 12 parts in the first 14 days to even see it. To find it, go to the middle of the lake and find the small archipelago that looks like a daisy on the map. Hit the egg in the center a few times, either yourself or by throwing Pikmin at it, and out pops the smokey progg, looking like something you might find in a used hanky. It doesn't seem very interested in attacking you, though it will if provoked, but instead it wants to investigate the onions for some reason. Let it make its way there so you can fight it on dry land.
To defeat it, you're better off keeping your attack force to between 10 and 20 Pikmin. Throw Pikmin on top of its head, then call them back when it shakes them off. Do what you can to keep your forces out of the smokey black ooze that it trails behind it, since it's highly toxic and will kill Pikmin that step in it. Replenish your attack force from reserves as needed and keep wearing it down until it gives up the ghost.
You don't get a part as a reward for defeating it, but you do get a pearl worth 100 seeds. Strategically, defeating it is more for bragging rights than anything else. At this point in the game you shouldn't need to be building up Pikmin numbers, just replacing losses and getting the Pikmin you have from leaf and bud stage to flower stage.
Repair-Type Bolt[edit]
This is a quick and easy part that you can get out of the way while you've got most of your Pikmin busy with walls, bridges, or bringing home parts. But only you know the trick. You might think that since it's on a high ledge that you'll want to use Yellows, but actually they aren't involved at all. Gather at least 20 Blues and lead them east to the left edge of the lake. There is a kind of walkway here, and a ledge to the left of it with water between them. Find the start of the ledge and throw your Pikmin on it. Start down the walkway and call the Pikmin; there's a railing on the ledge which keeps them from falling off, so they'll just follow you on the ledge as you head down the walkway. When you reach the end, direct your Pikmin to the middle of the platform there so they will find and start to carry the Repair-Type Bolt. You need to use Blues for this because when the part falls off the ledge most of the Pikmin carrying it will fall into the water; the fastest way back to the ship is through the pond anyway.
Massage Machine[edit]
This is an optional part, the first of two in this region. Take about 50 Blues and go south onto a peninsula. There is a new enemy here called the yellow wollywog which is basically just a tougher version of ones in The Forest Navel; fight them the same way. Bear left when you reach the end of the peninsula and continue through the pond to the start of a bridge. Clear the shearwigs in front of the bridge and start work on it. You may find something odd here; if a Blue finds a shearwig body already in the water then it won't hesitate to carry in through the pond back to the ship. But if it finds the body on land it will mill around in front of the bridge, refusing to go back to the ship until the bridge is finished. The same rule holds for any spoils and and the part in this area so you must complete the bridge to get the part. You may notice something else about the shearwigs in that they are allergic to water and lose health while flying over it.
While they are working, go back and pick up more Pikmin; mostly Reds for their fighting ability but some Yellows as well. When the bridge is done, cross and start exploring the area on the other side. There are some skulls here with bomb-rocks; load up on them so you can start clearing some walls if you have spare time. You meet a bulbear here as well. Bulbears are similar to bulborbs in that they come in both large and small varieties and you fight them in the same way. Bulbears are brown though and are somewhat harder to defeat. The Massage Machine is here in a corner on the right, so send it home with any spoils.
Interstellar Radio[edit]
Take a large force of Blues west along the shore of the pond. There is a new enemy you may meet on the way called the swooping snitchbug. It's a greenish insect which, as the name implies, swoops down on your Pikmin and grabs them. It does't really hurt them, but it will plant them back into the ground in some other location, and since presumably you don't want to be tracking down and plucking scattered Pikmin sprouts it's a good idea to try to get rid of them when you see them. You have to hit them in mid-air though so it can take a bit of doing. Once you've knocked them down they are usually pretty easy to swarm and defeat.
Turn south and the end of the shore and go through the pond to its southern end, clearing enemies as you go. There are two new enemies here; the first of which are the water dumples, basic predators that live in the water. They look a lot like the wogpoles we've seen earlier, but these are aggresive and, according to the game, relatives of the bulborbs. Fight them in pretty much the same way as the smaller bulborbs and they shouldn't be any harder to defeat.
Another new enemy here is the puffy blowhog. These are cousins of the fiery blowhogs in the Forest Navel. They are brightly colored, float in the air like a zeppelin, and instead of blowing fire at you they blow, well, air at at you. This doesn't sound scary but when you see dozens of your Pikmin blown off their feet in a swirl of lost petals you'll take them seriously. There are three of them scattered around the region, but this one has the Interstellar Radio.
To defeat it, start tossing Pikmin at it trying to keep as many as you can out of the way of its gusts of air. When one lands on it, it will weigh it down a bit so that it will be easier to hit with the next Pikmin. Eventually it will be forced to the ground where you can swarm it. It doesn't leave a corpse behind, just food pellets in random colors. Note that the gusts of air don't actually kill Pikmin, but stunning them, blowing them into other possible danger, and causing them to revert to leaf form is bad enough.
Once the blowhog has been defeated, send the radio back back along with spoils. They will go the reverse route of the one described to reach here, so your Pikmin shouldn't run into too many enemies on the way back.
Gluon Drive[edit]
Take a large party of mostly Blues west along the shore of the pond as for the Interstellar Radio. Include some Reds if your're going to be fighting bulbears on the way, and Yellows if you want to clear some walls for the next part. You can find bomb-rocks in a skull next to a stump about half way down. At the end you'll find two ends of a bridge; set Pikmin of any color to work on the near end and gather some Blues to continue on through the water. There is a yellow wollywog in this neighborhood so you'll want to get rid of it before it makes trouble. Find the other end of the bridge, clear the shearwigs away and start on it. The same rule about carrying spoils and parts applies here as for the area with the Massage Machine, so you'll need to finish both bridges before you can get the part. This is the heavyest part in the game, requiring 50 Pikmin to carry it, but fortunately you don't have to go that far and the route the Pikmin use to get it back is fairly obvious.
Zirconium Rotor[edit]
This is located just to the north of the Gluon Drive. You just need to knock down a lattice wall to get to it. There are a couple yellow wollywogs near it, so take care of those first or as you're working on the wall. If you've cleared the nearby solid wall on the way then the Pikmin will use this route on the way back. If not, they may take it though the ruins, and that means you'll have to clear the enemies from that area first.