The Distant Spring
This piece is to the East of the ship, along that narrow path above the water. You'll need to take your yellow Pikmin across that, 20 of them, and you may want to do it in turns, you'll probably lose a lot of them. Once they take it off the ledge quickly call them back. The rest of the trip is underwater, so its best to stop them right there. You can usually save quite a few. Then have the blues take it back to the ship.
East from the ship you'll notice a small peninsula, and on the other side will be some sticks for a bridge, take some blue Pikmin across and build the bridge. Then kill the big enemy there and take the Massage Machine back to the ship. Make sure you kill the frog on the peninsula before you send your Pikmin with the piece across it, or the frog will take the Pikmin out while they don't even have a chance.
First you have to get some bombs with your yellow Pikmin. There are some bombs near where you got the Massage Machine. Then take down the wall closest to the ship. Look on the map and head to the closest piece with a group of 10 yellow Pikmin. You need to throw your Pikmin up to the top, one level at a time. Throw them up, then head over to the ramp and climb up yourself. Then have the ten bring the UV Lamp back to the ship.
This one is also pretty simple. Head West of your ship, and find a bridge on the land side, and across the way where the Gluon Drive is you'll find the other half of the bridge. Just get some reds to build the one close and take some blues across the water to get started on the other half. Once they've both completed just have then take it back.
Along the way to the last piece you should have seen a stone wall that could be blown up. Blow it up and go through it with about 50 blue Pikmin. Kill all the frogs, and then take down the white wall. The Zirconium Rotor is in there.
The Bowsprit is located in the center of the level, and is being held by the giant spider. Kill all the enemies along the path to the spider and then kill the spider (using the same method as on the last spider you fought). Then take the peice back to the ship. In order to get the peice back to the ship you will have to build the bridge along the way, and take down the white wall. Make sure to take out the little bugs along the path too!
The Pilot's Seat is one of the easiest peices in the game. Now that you've found the Zirconium Rotor, all you have to do is continue down that path until you see a crater, look inside it to find the Pilot's Seat and haul the seat back to the ship.
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.
This last peice moves around the map, as you may have noticed. You obtain this peice by defeating the blue balloon enemy, that blows your Pikmin all over the place. All you have to do is take a bunch of blue Pikmin, use your map to find out where the enemy is, and when you find him, throw your Pikmin up onto him to attack. Once you get enough up they will weigh the enemy down so you can surround him for the kill. You reward is the Interstellar Radio. Just make sure your Pikmin arn't mauled on their way back to the space ship.