When you have defeated any of the following characters in 'Doubles' mode you will be able to play as them in exhibition mode.

Unlock Chad:
On the Junior courts beat him and Mason.

Unlock Chas:
In the Island Open beat him and Mel.

Unlock Dweezil:
In the Island Open defeat him and Mynx.

Unlock Flit:
On the Center court beat him and Emi.

Unlock Jet:
On the Junior courts beat him and Gary.

Unlock Kyle:
On the Junior courts beat him and Chris.

Unlock Linda:
On the Senior courts beat her and Shawn.

Unlock Meg:
On the Junior courts beat her and Sophia.

Unlock Mel:
In the Island Open beat her and Chas.

Unlock Micki:
On the Senior courts beat her and Kyoko.

Unlock Mynx:
In the Island Open beat her and Dweezil.

Unlock Shawn:
On the Senior courts beat him and Linda.

Unlock Sheri:
In the Island Open beat her and Willy.

Unlock Silvia:
On the Junior courts beat her and Sasha.

Unlock Skipper:
On the Center court beat him and Roy.

Unlock Bowser Star Character:
Beat Bowser in Peach Tournament

Unlock Waluigi Star Character:
Beat Waluigi in Peach Tournament

Unlock Mario Star Character:
Beat Mario in Peach tournament

Unlock Peach Star Character:
Beat Peach in Peach Tournament

Unlock Luigi Star Character:
Beat Luigi in Peach tournament

Unlock DK Star Character:
Beat DK in Peach Tournament

Unlock Peach Dome Court:
Beat the Peach Tournament in either Singles or Doubles

Unlock Mini-games section:
Raise Clay (aka Max) or Ace's (aka Tina's) Level to 2

Unlock Max Level (Level 5):
On Level 4 in Exhibition mode beat all the characters with one character