After Mario defeat Bowser in the Dark World, use the 1st key to open the door to the basement. The door marked with a star to the right of the entrance to stage 7 opens to the room with a pond of metallic liquid.
The first star is located on the island in the middle of a lake. Jump on to the swimming creature and run up to its head. If you find it difficult to get to his head, try this: Pound on its back, and it will lower its head, and Mario can walk onto it easily! It will move according to which direction Mario is facing. Then jump over to the island to collect the star.
Collect 8 red coins. All of them are in the large area with moving platforms running above.
Turn Mario into Metal Mario using the green ! box when getting off from the elevator to the lake. Then walk down into water along the path and step on the ! switch. Then go through the opened gate and jump across two big gaps for the star.
In the toxic maze, perform backward jump at the wall with green stuff. It is near those bats.
The top blue circle on the map before Mario drops into this toxic area corresponds to the position of this door.
In the toxic maze, perform backward jump near the 3 consecutive blue coins. After taking the elevator, climb on red grid at the ceiling to get the star. The position of this door corresponds to the left blue circle on the map of the toxic maze.
In the room where giant rocks are rolling out, the star is hidden above just before the door leaving the room which is after the big white arrow on the wall,. Perform wall-jump to get the star.