Breaking into Bowser's Castle
Follow the walkway forward, jumping over the Dry Bones and avoiding the fire wheel until you start running up the wall. Continue on past two more fire wheels, then quickly keep going past the Magikoopa, as it's not worth the effort to kill. Up the path past another Dry Bones is a double fire while with a wooden platform on the other side. If you follow the fire wheel around staying between its spokes, you can grab a Life Mushroom. Use the wooden platform to get across the lava, being careful to jump between the fireballs on the other side. Go around the fireball in the middle of the path and turn the corner where you can quickly run up and stomp the Magikoopa before it can attack. Past the Magikoopa, use the wooden platform to cross another section of lava, but don't stay on it for long, because it sinks into the lava. When it turns into a side-scroller, grab the checkpoint farther up the path.
Just past the checkpoint is the Comet Medal above the breakable brick, then a couple lava jumps with fireballs shooting up. Be careful right before you go up the wall not to run into the fire wheel. Head up the wall on the right being careful to wait for the fireballs to land back in the lava before attempting to jump over the pits. You'll keep going around to the ceiling with some more lava pits, then a fire wheel at the end where it turns back up to a wall. Keep going up the wall and you'll see a large fire wheel with a 1-Up Mushroom at the top encased in water. Jump up into the water and swim around between the spokes of the fire wheel, optionally going all the way around the circle to grab the 1-Up. In the next circular room is a ? Coin which will create a circle of coins around the three-spoked fire wheel in the next room. Time when you get the ? Coin so that you can immediately get in between the fire wheel and go around in a circle collecting all the coins for another 1-Up. Past the last fire wheel is one more room with just a Cheep Cheep in it, then you can swim out of the water and grab the next checkpoint.
At the checkpoint flag you can backflip and spin to get up on the castle wall behind you, then wall jump and spin for another 1-Up Mushroom. Continuing on down the path are two Whomps and an open area with another 1-Up Mushroom in it. You can slide under the Whomps and stomp them for star bits, or just keep moving. Past the Whomps you'll continue up some stairs then turn a corner and the path will take you to a Goomba with a Dry Bones on the ledge above. Keep going around and you'll come to another Goomba on the step above, but this one you'll need to jump and spin to get above. When you get to the top, jump to the platform below you and gravity will switch so you're standing on a squarish platform with a fire wheel spinning in the center. You can go left or right, but you need to get down to the lower left corner where you can jump over to the next platform with a fire wheel in the center. On this one you need to go around it clockwise, jumping over the moving platforms and the tips of the fire wheel. At the bottom is the Launch Star, but if you keep going all the way around you can get another 1-Up Mushroom.
You'll launch to a little platform with a shining meteor and a couple crystals. The crystal on the right has a Life Mushroom in it if you need it, and you can ground pound the meteors into the three locks on the door in front of you to break it and open the doors. When you do, you'll be sucked into the throne room again and Bowser will show up. After a short conversation, you'll go to the boss fight planet to face him.
This fight is very similar to the last time you faced him in Bowser's Lava Lair, with a few differences. He starts out with a couple ground punches, and this time they produce purple shockwaves that circle the planet. Just jump over them and he'll start calling down the meteors. The meteors also create the purple shockwaves when they land and you'll have to jump over them while there are multiple shockwaves on the planet. Keep moving and try to jump back towards the meteors over the first shockwave so you're in good position to jump the next one. While you're doing this, Bowser will be looking for you with his big circle of light to perform another ground punch. Like last time, you want to get as close to the meteors as possible without him breaking them. When he punches the meteors will rise from the planet and you can jump on one and ground pound it into him.
The cycle starts over again with a ground punch, then meteors, then another ground punch, so do the same thing and ground pound another one into him. After that he gets angry and his attack cycle changes a bit. This time he starts off with the meteors, then chases you while breathing fire down on the planet while you're trying to avoid the meteors' shockwaves. It's harder not to get hit here, but the trade off is you can more easily get in a good position for the ground punch. As soon as his fire stops, quickly get into position near the meteors so you're ready to go when his punch lands. Ground pound one the meteors into him, then complete his angry cycle one more time to finish the fight off with the fourth meteor you slam into him. Back in the throne room, Bowser will take off and you can go grab the Grand Star and open up the next world.
Gravity Star Speed Run (Prankster Comet)
You have to repeat most of the previous star within a time limit. You start with a time limit of 30 seconds but can pick up time extensions along the way. Run up the walkway past the Dry Bones and fire wheel, then up the wall grabbing the bonus timer on the left between the next two fire wheels. Ignore the Magikoopa up the path and don't bother going for the Life Mushroom on the other side of the next fire wheel, just continue through over the wooden platform and grab the bonus timer over the grate while trying not to get hit by the fireball that comes shooting up below it. Head up the stairs and long jump the gap next to the Magikoopa and keep going into the 2D section. At the top of the stairs, run past the block and quickly sideflip back up to the bonus timer above it before moving on. Make your way over the lava pits, collecting another bonus timer when you start going up the wall. After the ceiling going up the next wall, backflip up onto the blocks out to the left and again to the bonus timer, then continue on. Jump into the water on the right side of the fire wheel spoke at the top and spin to quickly swim into the bonus timer in the next room. Get around the next fire wheel and you can get another bonus timer on your way out of the water.
Collect the bonus timer before heading down the path to the Whomps and be sure to slide under their legs with . Grab the next bonus timer in the upper left corner of the area with the Whomps, then continue down the path at the bottom. Jump all the way over the Goomba to the platform with the next bonus timer and make sure you're spinning when you jump at the next Goomba so you don't waste time getting knocked down. Quickly jump to the next platform and go left, which is shorter and allows you to pick up another bonus timer. Backflip over to the next platform and head down clockwise all the way around. You'll pick up another bonus timer at the bottom where the Launch Star was in the previous star, and at the top of the other side you can get the Power Star by wall jumping off the fence.
After using the wooden platform to get across the lava right before turning the corner and heading up the second Magikoopa, you'll find the first Green Star. Right after you go past the grate with the coin on it that a fireball jumps up from you can barely see a small stone tower off in the lava to your left across from the stairs. At the edge of the walkway, backflip and spin out to the tower then jump up and collect the star. After coming out of the water section, jump on top of the ? Block after the checkpoint flag and backflip and spin up to the second Green Star.