The Forest of Hope
Eternal Fuel Dynamo
Take your Pikmin and bash your way through the first white wall. Just throw the Pikmin at it and they will do it by themselves. Once outside you'll find a few enemies, quite a few flowers, and the Eternal Fuel Dynamo.
Once you go through that first white gate, you'll notice on a ledge to the left a 5 Pellet. Throw a few Pikmin up there to take the pellet back, then throw all the rest up there. To the left you'll see a passage up a root that goes through water. By throwing your red pikmin up on the ledge they will not have to go through the water, which they can't because they can't swim, so you can get the Shock Absorber right off the bat. Just beat that big dude sitting up there, and then let you Pikmin haul the Shock Absorber away, they'll take it off the ledge without drowning themselves.
Whimsical Radar (yellow Pikmin required)
Head to where you found the yellow Pikmin. Bomb and then head through the closest rock wall to that area. As you walk through you'll notice something up on the ledge. If you don't make your camera angle wider. You'll need yellow Pikmin to be able to reach it, and you'll need 20 of them. Throw them up there and they will take it back to the ship. Just make sure the path is totally clear. Sometimes they take the path you don't want them too.
If you head North West from the ship (check your map (now that you have the radar) If you don't know where that is) you'll find a dark black door. Break through it and take the Nova Blaster back to your ship.
Extraordinary Bolt (yellow Pikmin required)
In the far West of the map you will see a huge wall that is pure black, and that your Pikmin cannot hit. You need to bomb it nine times to take it down. Start by taking the bombs from the close up bucket, and the next closest ones are where you found the first ship peice, the Eternal Fuel Dynamo. After you've bombed it until it has come down just have your Pikmin ship it back to the ship. (It takes 30 Pikmin)
Make a team, your lookin for about 70 red and 10 blue Pikmin. Head towards where you found the yellow Pikmin Onion, and then take a left. You'll find a bunch of bad guys, a box, and some water. Once you've defeated all the enemies take the blue Pikmin, head into the water, and then throw them to the backside of the box. Once they've pushed it out of the way use the C-stick to carefully take your Pikmin team across the narrow path. It works best if you take them across half and half. Make sure you don't venture to far in until you've gotten them all across though, the boss may start eating your Pikmin! Next fight the boss ;). This boss is actually really easy if you know what your doing. The basic principle to remember is that Pikmin attack much more effectivly if they are on the enemies head or back, thrown up. So the best times to strike the boss is right when its coming up. As soon as you see its beak emurge use the C-stick to center the Pikmin around it. They should all grab hold of his head, and the ones that don't will grab ahold of its body. They will take each one down much, much quicker. The last Bird will release the Geiger Counter. Make sure the path is 100% clear before you start packin stuff home!
PS: The bosses might have wiped a couple of flowers off your Pikmins heads, there's some grass in this area.
Radiation Canopy (blue Pikmin required)
Time to assemble another team, your in the big leagues now. Take about 40 reds and 20 blues. Head North, and you'll find a ledge with some grass on there, and you'll have to fight a big dude and a little dude along the way. Forget taking the two carcases back to base for now. Throw the red Pikmin up on the ledge, they can't swim. Take the blue pikmin and go through where the big black gate used to be and you'll see a small white gate in some water. Get the blues to start takin it down and help them by attacking it too. Faster the better. Once you get up start taking down the next wall with all the Pikmin. This boss can be incredibly difficult, and don't be upset if you have to or want to try again. You may lose a lot of Pikmin. Watch out for his bombs! He hurls these huge rock things at any Pikmin he sees, but first he sucks in. Make sure your not in the way of his shot, or even better, throw a Pikmin in. It's how you defeat him. Throw a Pikmin into the little hole that starts sucking in air and then he will overheat and expose the shiny body part. Then run behind him and launch a bumch of Pikmin up there. Once he's dead you can take the Radiation Canopy back to the ship, assuming you've killed all the bad guys along the way.
The Chronos Reactor is located at the far North of the map. Take about 30 Blue Pikmin with you and find a square platform with a yellow flower on top of it. Throw the blue Pikmin up onto the platform, then find the little water spout to get yourself up. Throw all the blue Pikmin into the flower. This will convert them to yellow Pikmin. Then jump down onto the beach to the North with your yellow Pikmin. When they start drowning just whistle at them, over and over again, until they slowly swim towards you. Whistling gives them motivation. Then throw the yellow Pikmin up the ledge to grab the peice. Once they haul it down, stop them, throw them all into the blue flower and then have them carry the peice all the way back to the ship.
#2 Ionium Jet
Also, at the far north of the map, you will find the second Ionium Jet. You can collect it by taking 15 blue Pikmin, throwing up to the ledge (The ledge that you can get to the top of using the jet stream of water) and then throwing them eastward towards the peice of ship. Have them haul it all the way back.
Sagittarius (blue Pikmin required)
All you need to get this peice is a flock of blue Pikmin. Take the Pikmin and head out to the lake, the lake close to where you found the Eternal Fuel Dynamo. Take them across the lake and you'll see the ship piece lying on the little isle near the back. Kill all the enemies along the path back to the ship, and take your Pikmin down to the isle where the ship peice is. Throw the Pikmin up onto that isle so they'll start building the bridge, and once they're done send them to the other side to build that bridge, and when both bridges are completed get them to take the peice back to the ship and your done.