Here is the list of stages, along with info about them of Yoshi's Island:Baby Luigi Time!
World 1:The plain Plains (Yup, the name is a pun)
The first world in the game is mostly made of plains and basic biomes like caverns and aerial zones.
1-1:Jump High with Baby Luigi!
The stage is a normal plain level, with a few grass-covered hills in the background. The first thing you encounter is a quite high wall you can jump over. It has a few Shy Guys on it you can swallow for eggs. Near the Shy Guys, you can hit a Winged Cloud to make stair cases leading to the Big Star. You then see a deep hole with a bunch of Nipper Plant inside it, as well as a wall blocking the way, so you need to pass under the wall. A Winged Cloud makes a Chain Chomp ball appear, so it is recommanded to pop it and crush the Nipper Plants with the rock. You then have to just pass under the wall. After that, the stage is mostly just shy guys and high walls. The last thing you'll encounter before the Goal Ring is a stack of Shy Guys. Once they are out of the way, you can finish the stage.
1-2:The Waterfall Cave.
The stage is a cave stage with waterfalls in the background. It has odd enemy placement, so some people think the enemies were once different. It is also very long, but easy in return. The first thing you see is a few Goombas(most of them spawning in the sky) walking around. You can try stomping them, but it won't do much, so just avoid or swallow them. Then, you find a few holes you need to jump over. One of them actually has a pipe in it through. It lets you skip a big part of the stage and leads to the Big Star as well. If you don't use it through, you find a lake with Cheep-Cheeps in it. Once you pass through them, you find a new transformation introduced in the game, Dragon Yoshi. Use it to destroy a wall of otherwise unbreakable bricks. Then, turn back to Yoshi and then pass through an area with a few water puddles, and Slime Drops as well. If you took the pipe, this is where it leads you. There is another pipe after, leading you to an outside area with a few more Goombas. Once you pass them, you see the Goal Ring.
This stage is very similar to "Boing!" from Yoshi Island DS, through it takes place more near the ground. It is basically just hills with a bunch of Bouncies on them, with a few Koopa Troopas and Shy Guys. There is also a area where you find an army of Mildes and Large Mildes. By hitting a Winged Cloud in that area, you can make an huge flower appear. Jump on the leaves of the flowers to reach the Big Star. After that, you see the Goal Ring.
1-4:Carl the Cannonical Kaboomba's Fortress
As the name indicate, the stage is full of Kaboombas. It also has a lot of Bullet Bills, and cannons that shoot you around. The first part of the stage contains Bullet Bills and Kaboombas, with a few bottomless pits. You then need to jump on rotating platforms with spikes under them. You then enter a door to the second part of the fortress. It has cannons that will shoot you on platforms in the sky, but beware of the Kaboomba on them! But sure to try timing well when you enter the cannon if you don't want to get hit. If you fall below, you need to restart from the beggining of the area! The last and final area contains rising spikes. Be sure to avoid them while you jump on the various platforms and use cannons! You then enter the boss room, with Carl the Cannonical Kaboomba inside.
1-5: The Band of Bandits
If you hate bandits, then you'll absolutely hate this stage. It is full of bandits, with occasionally shy guys as well. It takes place in fortress ruins in a forest. The first section takes place on grass, with tall walls, including one that needs you to hit a Winged Cloud to make staircase appear, but be sure to take the Big Star in the wall's secret cave! You then jump on some platforms to enter ruins in the sky, with of course bandits everywhere. In the ruins, there are two paths: The Sky Path and the Ruin Path. The Sky Path introduces Fly-Bandits, who are yellow Bandits with a propeler on thier head. They are even more annoying than normal ones! It is shorter through. The Ruin Path takes place in the ruins. It has less bandits than the sky path, but is much longer. In the end, you fall back the the ground...And you see an ENORMOUS army of bandits running after you! Quick, go to the Goal Ring!
1-6: Hover the Snifit Army
Yet another stage in the sky, Snifits are plenty here. It also introduce Fly-Snifits, who are flying snifits, and Dual Snifits, who are Snifits with two cannons instead of one. It is by far considered to be the hardest stage in World 1. In the first part of the stage, you are freefalling while there are flying snifits around. After that, you need to Flutter Jump to different platforms until you reach a pipe that leads you to a flying airship with a bunch of snifits in it, with a few Dual Snifits at the end. Then, you enter the second part. You enter a small flying island with a swamp in it, meaning that there are Wigglers and Slime Drop around. After beating them, you see a pipe with snifits coming out of it. After passing it, you find the last obstacle, a bunch of Fly-Snifits and Dual Snifits. After that, you can go in a forest and jump in the middle ring. But if you don't jump in the middle ring, you can get past it to get the Big Star!
1-7: Goonie and Trees
This stage basically continues the stage before it. There are a lot of Goonies here, and all of thier variants are present but skeleton ones. You start in a forest area with a few flightless Goonies, along with hills with Bowling Goonies rolling on them. After that, you see a row of Goonies. If you jump on those, you can reach the Big Star of the stage. If you ignore them, go on and you find a small lake with the new Tuba Goonies, goonies with tubas that live normally underwater, along with a few Cheep-Cheeps. After that, you find an Helicopter Transformation. Use it to fly in the sky and reach the Yoshi Block on another flying island, but be sure to avoid the Goonies flying in the sky. In the last area, you see a few Fuzzies flying around. Yoshi becomes dizzy if you touch one! Just rush through the area and reach the Goal Ring.
1-8: Tower of Rovbi the Fuzzylator
This stage is quite special for a tower stage: It contains Fuzzies! It is basically a series of rooms, with more and more of them in each room. At first, there are very few Fuzzies. You have to jump on some moving platforms before reaching a door. After that, there are more Fuzzies, and there are a few Cannons that will shoot you in the sky. You then need to Flutter Jump to the door. The next area consists of reaching a giant Fuzzy statue with a door. To do so, you need to swallow the various Shy Guys in the room and throw an Egg at the Flying Cloud. It will cause stairs to appear. Jump to the door on the fuzzy statue, but be sure to be careful about the Bandits on it! The next room, and by far the hardest is full of Fuzzies and you need to jump on a rotating platform, through there are Fly-Bandits flying in the sky to annoy you, as well as spikes on the ground and the walls. Go in the door, and reach the last room(not counting boss room). It is just a path to the boss room, that is at the top of the tower. The boss is obviously Rovbi the Fuzzylator.
World 2:Disasterous Hills
2-1: Geyser Desert!
The first stage of world 2 introduces the Geyser obstacle, as well as Geylies, who are small geysers with two legs and eyes. You start in an area with a fallen tower in. It is quite similar to the first area of 1-8, but with no fuzzies or moving platforms. Instead, there are Geylies around. Jump on them to they lauch you to the door. Go in the door, and you find yourself in a desert. A volcano can be seen in the background. You can also be propulsed in the sky by the geysers, usually resulting in you hitting a Fly-Guy, through one of them leads to the Big Star. After passing the room, you enter a cave flooded with water. You are in a maze: There are 5 pipes, but only one leads to the exit. Otherwise, it sends you back to the desert area. After finding the right pipe, jump in the Goal Ring to finish the stage.
2-2: Danger! Tall Heights!
Another stage, this time in a mountain chain. It also autoscrolls through the stage. In the first area, you must jump on rotating platforms while avoiding the various Parakoopas. You then jump on a moving platforms for about half of the stage. There are multiple Wild Ptooie Piranha throwing Needlenoses at you. Jump on one of the hills they appear on to get to Big Star. If you don't manage to get back to the platform after through, you're forced to lose a life. The last area after that takes place on one of the mountains. Flightless Goonies are runing around while you must try to get to the top of the mountain. On the top of the mountain, you encounter a few Piranha Plants before jumping in the Goal Ring.
2-3: Pebbles and Stones
This level takes place in a cave with a lot of spikes in it. The first area takes place on a row on spikes. You must move a Chain Chomp Rock by standing at it's sides. By jumping on a bunch of falling platform, you can reach a star, allowing you to play as Super Baby Luigi! You only have a few seconds to get to the end of the area with it through. You then enter a cave with lava, as well as a flying cloud and a few Fangs. Lauch a egg at the flying cloud to make a Skull Raft appear over the lava. Jump on it and fight off the various Lava Drops in the area. By hitting a flying cloud with right timing, you can make the Big Star appear. Then go in a pipe to enter a dark cave with torches around. Invisible Boos(due to the dark) maybe attack you, but you can see thier eyes. After this area, the cave lights up, revealing the Goal Ring.