After you sneak into Nimbus Castle and get past Dodo, you find the key to the room where Birdo awaits.
Birdo doesn't have any weaknesses, and is strong against many types of attacks. Birdo is affected normally by Jump, Thunder, and Ice, so use those types of attacks if you wish. Birdo can spit eggs at a character, which does moderate damage. Birdo also has a single egg attack that does high damage.
After you defeat Birdo, you get Castle Key 2, so check on the northeast door to unlock it, and go through. In this room, wait for the Pinwheel to stop spinning before you try to run past (or just defeat it) to avoid getting knocked down into the lower area. (If you fall below, just go southwest until you're in the hallway with three doors, and go through the middle door) Also in this room, you can try to carefully jump on top of the chest, and jump to find a hidden chest that contains a Frog Coin. Then get past the Jawful (or defeat it) and go through the northeast door.
In this hallway, check on the northwest door and there will be a cutscene. Afterward, go through the northeast door. Interact with the Heavy Troopa to start the battle, and use Jump attacks as before. After that, go through the door and there will be a cutscene.
Afterward, go through the door where Valentina went, get past the Bluebirds and go to the next room, stand beneath the treasure chest and jump to reveal a hidden platform, jump onto the platform, then jump to open the chest that contains a star. You can either run northeast to the next room and use the star to instantly defeat Dodo, or you can try to run southwest to the previous room, defeat those two Bluebirds, then quickly go northeast to defeat the remaining Bluebirds and Dodo before the star wears off. Otherwise, you can battle Dodo, or just let Dodo go through the door to avoid fighting him.
After you get past Dodo, go northeast and you will fall all the way down to where two guards are blocking the hot spring. Before you continue, you might want to change your party members to Geno and Bowser. When you're ready, use the smiley springs to go up to the main part of Nimbus Land. There will be a cutscene and you will have to battle Valentina and Dodo.