Battlerock Galaxy is accessible from the Fountain observation dome. You need 12 Stars to enter.
Star 1: Battlerock Barrage
You can use the Bullet Bills to break the glass cages on the saucers. Position yourself so that the glass cage is between yourself and the Bullet Bill. Then move so that the bullet hits glass and not you
Star 2: Breaking into the Battlerock
There is a hidden star on this level. For the time being, ignore the Hungry Luma you meet.
Star 3: Topmaniac and the Topman Tribe
In this level you will reach a Luma Shop to buy either a 1-Up Mushroom or a Life Mushroom for 30 Star Bits. The Life Mushroom might be useful if you need help during the upcoming boss fight.The life mushroom gives you three extra lives
Boss fight: Topmaniac. Jump on Topmaniac then spin him into the force field. Repeat twice more.
Star 4 (Daredevil Comet): Topmaniac's Daredevil Run
Available when a Prankster Comet is in this Galaxy.
This is a repeat of the boss fight from Star 3, except you only have one life point.
Star 5 (Purple Comet): Purple Coins on the Battlerock
Available when a Purple Comet is in this Galaxy.
You need to collect 100 Purple Coins, while traveling through the level on an automatically moving saucer. There is no time limit but you will only get one chance to obtain most of the coins, so the pressure is on.
Follow the path of the coins, moving around and above and below the saucer and jumping as appropriate, while avoiding the electrified walls, rotating spheres on the saucer, and the balls that get fired at you. You'll need to jump over a couple of electrified walls, the first of which is an easy jump, but the second will require a Backflip.
Once you have all 100 Purple Coins, collect the Star.
Star 6 (Hidden): Battlerock's Garbage Dump
Enter Star 2. Collect at least 30 Star Bits from the flying saucers at the start. Proceed through the level as before until you reach the Hungry Luma. Feed it 30 Star Bits to transform it into a new planet, and use the new red Launch Star to fly to this planet.
Here you will be asked to clear all the garbage, which you will need to do within 30 seconds. To do this, pick up bombs then throw them (by performing a Spin Attack) at the garbage. As time is short you will need to throw the bombs such that they will do the maximum amount of damage. Helpfully, there are some yellow spots on the floor, and if you can aim throw the bombs so that they land near these spots, you should be able to destroy all the garbage in time. The yellow spots, by the way, are coins embedded in the floor which can be released by being shot at with Star Bits.
Once all the garbage has been destroyed, collect the Star.
Star 7 (Hidden Luigi, Green): Luigi under the Saucer
This is one of the Hidden Luigi Stars, available after Luigi sends you a letter with a photograph of this galaxy. In addition, this is one of the three Green Stars, which you need to collect to unlock the Trial Galaxies.
Enter Star 1. Proceed through the level exactly as for Star 1 until you get right to the end. Instead of collecting the Star on the top side of the saucer, release Luigi from the glass cage on the underside of the saucer, using Bullet Bills as before. Talk to Luigi and he will give you the Green Star.