Use all 16 characters and beat star cup, doubles and singles. When that's done, go look at the characters and use the "star" near them to enter the "Star Tournament".
Birdo and Yoshi court
Beat star cup doubles mode with Birdo.
Wario and Waluigi court
Beat every cup with Wario doubles tournament
Ring shot easy win
Get 40 points then just stand there and let every ball go past you until your opponent gets 40 points and ties with you then you get as many rings as you can and win the next point then let next ball pass and repeat those steps so you keep tying.
Two unlock the second Mario Bros. court you will need to beat the star tournament with all 16 characters. This court is in the court yard of Peach's Castle.
Unlock Donkey Kong Court
Unlock this court by winning the Mushroom Cup/Singles Tournament with Donkey Kong.
Unlock Yoshi and Baby Mario court
You can get this court if you win the Mushroom Cup/Singles Tournament using Yoshi.
Unlock Shy Guy
Unlock Shy Guy by winning the Star Cup/Singles Tournament.
Unlock Donkey Kong Jr.
You can unlock Donkey Kong Jr. by winning the Star Cup/Doubles Tournament.
Mario Bros. Court
Unlock Mario Brothers Court by winning the mushroom cup/singles tournament with Mario.
2nd Mario Bros. Court
Unlock the 2nd Mario Bros. court by winning the mushroom cup/doubles tournament with Mario
New Court In One-Player Mode
Go to the game with the tennis ball spitting piranha plants, get a perfect score (all the balls), and go back after exiting. A new court should be there for the piranha plant game.
New Computer Opponent Level
After getting the "Star Tournament", use all 16 characters and beat all cups (rainbow, moonlight, planet) to get the "MAX" difficulty
level of your computer opponents. Use it, if you think the computer players don't offer much of a challenge... But at that level, they're going to kill you.
Unlock Rainbow, Moon, Planet Cup
To unlock the Rainbow Cup you will have to beat the Star Cup with all characters. Then when you go to the character select screen you will need to hold R when you select your character. The game menu will come up with a star on top of the cup in tournament mode. This mode is the same as the normal mode except that it has different names. this is the order; Rainbow Cup, Moon Cup, Planet Cup.