Dreadnought Galaxy is accessible from the Garden observation dome. You need 48 Stars to enter.
Star 1: Infiltrating the Dreadnought
You start on an hourglass-shaped planet. Use the launch opposite where you start.
This takes you to an area with some helmit-wearing goombas. Kill the goombas by spinning next to them and jumping on them when they are upside-down. Then go in the pipe.
The pipe takes you to a 2nd area. Go right until you find a raised platform between two moving walls. Wall jump to get above the walls. Grab the Life Mushroom on the left. Then run to the right past the moving floors and activate the green switch by spinning next to it. It will turn red, and the level will rotate 90 degrees counter-clockwise. Use wall jumps to get above what are now moving walls, and go right. Activate the green switch. Use the springs to go up and to the right into the pipe.
Jump on the green topmen to get above the rotating cylindars. Stand on the raised platform ahead. You should see a wall moving up and down on either side of it. Use wall jumps to get on top of these walls, then use the Launch Star above.
You will land on a cube-shaped planet. Use the Sling Star opposite where you land.
You will land on a spherial planet with some raised platforms. Flood the planet using a Bullet Bill to break open a cage containing a fountain on its surface. Climb the green staircase, and jump on the moving platform to the right. Keep moving along these platforms to get to the star.
Star 2: Dreadnought's Colossal Cannons
First, mount the nuts in front of you and cause it to turn by standing on the right side until you start to fall, then walking/running to the right, so you end up staying in the same place as the nuts move forward. Dismount when you've reached the opposite side. Turn all of the blue switches yellow in the first area by walking on them, but avoid the unchained Chomps. Once they're all yellow, they'll turn green, and the electric fence will turn off. Turn all of these switches yellow, and again they'll turn green and all the Chomps will turn into Star Bits. Mount the nuts ahead, and use the same method as before to move forward, then dismount the ones you were on and mount the nuts to your left. Same method to move forward, but beware of the watermelon shooting enemies. Spin by a watermelon to shoot it back at them. Once onto land again, you can hit the two ? Blocks to get Star Bits, and Coins, but beware the Bob-Ombs. Use the Launch Star to arrive at a mechanical platform. Mount it. Avoid the first shooting cannons and electric fences. Jump onto a yellow platform to get a Coin and avoid falling off. Get back on the still moving platform. Avoid two cannons before you come to an upside down moving platform. Mount it and beware of the Goomba. Again, avoid the cannons and electric fences. Climb the upside down stairs and hit the ? Block to get Star Bits. Avoid more cannons before this platform breaks down, and you must jump back to a normal moving platform. Kill the Goomba quick, and mount the solid yellow platform with a Thwomp. If you dare, jump on top of the Thwomp to get a 1-Up Mushroom. Jump over an electric fence to a smaller yellow unmoving platform, and back onto your moving platform. Avoid two cannons before, once again, your platform breaks down. This time, you must mount a sideways platform. Kill the Goomba, and avoid cannons. Jump over an unmoving platform and get the ? Block if you dare. Mount another upside down platform. Avoid cannons and fences yada yada. Jump down to a normal gravity platform and mount the regular moving platform. This is where it gets crazy. Try, if you can to stay on the unmoving platforms by Long Jumping across the gaps, but avoid the electric fences. Once again, return to the moving platform. Avoid the laser rings, but stay on the platform. The second Purple Laser Shooter you see you must jump on to, when the platform gets there, and it will launch you right into the Power Star.
Star 3: Revenge of the Topman Tribe
There is a hidden Star here. For the time being, DO NOT enter the pipe on the opposite side of the first flying saucer. Jump twice on the Green Topman to get yourself to a Sling Star. This will take you to a small planet with a caged Luma. Spin the two Red Topmen into the electric fence to kill them and release the Luma. If you want, there is a 1-Up Mushroom on the tallest pillar of the planet. Use the pillar next to it, then jump-spin to reach it. Talk to the Luma. It will transform into a Sling Star. The Sling Star will take you to a cube planet. On here is a Green Topman, and a red button. Jump on the Green Topman to grab the 1-Up Mushroom located high aboe one of the sides. Ground pound the button and collect the blue star pieces scattered about the planet. They will make 2 Pull Stars and a Launch Star. Pull yourself to the Launch Star and spin to travel. You will land on a rocket. Run under it to get a Red 6-Life Mushroom. Now, use the Pull Stars to navigate through the cannons and mines. you can shoot the mines with Star Bits to make them blow up, and go away. At the end there is a Launch Star. Use it. You will come to a long blue planet with lots of purple laser shooting enemies. Their lasers only go as far as the white rings on the ground, so use that knowledge as you will. On the left, there's a Green Koopa Troopa. Jump on it to obtain it's shell, then shake to shoot the shell at the chest ahead of you to reveal a coin. There's another chest after that with Star Bits, so you can go get another Koopa Shell if you want. The is a third chest at the very end containing a 1-Up Mushroom, and you should probably grab that. The Koopa reappears after you kill it, so you have unlimited shells. Use the Launch Star at the end to go to the boss planet.
Spin the Topmen into the electric fence if you want, or just go around them to the top of the planet. Enter the arena, and a large Topman and two red Topmen fall from the sky. Spin the Red Topmen into the electric fence, and jump on the large Topman to make its blades retract, and spin him into the fence too. Do this three times to get the Power Star. If you need it, on the opposite side of the arena from the steps, you can buy a 1-Up Mushroom or a 6-Life Mushroom from the Luma salesman.
(Pictures coming soon)
Star 4 (Speedy Comet): Topman Tribe Speed Run
Same as Star 3, with a six minute time limit.
Star 5 (Purple Comet): Battlestation's Purple Coins
This Star is rather like Star 5 from the Battlerock Galaxy.
Star 6 (Hidden): Dreadnought's Garbage Dump
Enter Star 3. At the start of the level, go to the opposite side of the flying saucer where you are standing, and enter the pipe.
Talk to the robot. It will ask you to blow up the trash. You will have 30 seconds to do this. This is similar to, but harder than, Star 6 from the Battlerock Galaxy.
You should be able to blow up all the garbage within the time limit by placing a Bob-omb at each of the five red dots shown on the diagram. The blast radius of each Bob-omb is shown as a circle in the diagram.
Each Bob-omb will blow up ten seconds after you pick it up. That means that any Bob-omb you pick up when the timer is at ten seconds or less will not detonate on its own. If you place a Bob-omb within the blast radius of another Bob-omb, it will detonate; you can use this trick to extend the range of the last few Bob-ombs you place, in case you throw them too far from the target. Alternatively, as long as you pick up the last Bob-omb with more than 10 seconds on the clock, you know that you have quite some time to place it carefully in position - you do not need to throw the last Bob-omb wildly.