Bowser Jr.'s Lava Reactor is accessible from the Engine Room observation dome. You need 45 Stars to enter.
This galaxy contains a large central lava planet with smaller planets around it.
Star 1 (Grand): King Kaliente's Spicy Return
You start on the outside of a hollow planet with a black hole in the middle. You need to get a Bullet Bill to break the glass cage holding the Launch Star. As you progress round this planet towards the Bullet Bill, kill all the Goombas so they don't get in the way when the Bullet Bill is chasing you. Jump to the platform with the Goombas and then to the next platform. Follow the path of stones until you reach the Bullet Bill cannon. Make one follow you to the Launch Star and use it.
You will fly to a set of green platforms on the main planet. The platforms will sink into the lava as you stand on them, but you can minimise this by jumping. Two enemies fire melons at you. Spin these back at them to defeat them and reveal a Launch Star. You will fly to another set of green sinking platforms laid out in a large circle.
Boss fight - King Kaliente. This boss fight is the same as before (Star 3 in the Good Egg Galaxy), except it is harder because of sinking platforms and you have to spin the melon more times.
When Kaliente is defeated, collect the Grand Star, which as well as increasing your Star total will unlock the Gate and Garden domes.