Defeat the Bosses in any two Worlds to unlock time attack mode.
Collect all 35 Stars to unlock a bonus board in Bowser's Castle.
Use the following steps to reach the corresponding Boss:
The Plant: Go inside the windmill on the first level.
The Fish: Go on the ice level. Go into the second door and you will see an iceberg. Knock it straight up to create a hole. Go inside and there should be a ship. To open it, open the three treasure chests.
The Sphinx: Go through the second door on the sand level. When u go through, you will see the top of a pyramid. Hit the lions on both sides to make it appear. Go inside, and there will be three switches. The one to both left and right will have arrows. Hit which ever one desired. Either hole will appear. Go inside and you should see two switches again. Look for the arrows. If done correctly, you will get to that Boss.
Big Boo: On the starting screen of where the fair is located, you will see a house with closed doors. Get one star to enter it. Inside, there is a door. You will need 10 stars to get into it and reach Big Boo.
Bowser: For each Boss that you defeat, you will get a key. Deliver the four keys to the mountain to enter it. You will need fifteen stars to get to him.