Booty Calls hosts occasional tournaments which reward you with daily goodies if you reach a certain rank, as well as an exclusive new character if you manage to fulfill the tournament's requirement. To access it, click/tap the Tournament button on the main game screen:

In order to complete the tournament and unlock the exclusive character, you need to gather all puzzle pieces that complete the gray image below.

Puzzle pieces are awarded daily in accordance to your rank among all of Booty Calls's players.

To get a higher rank and more puzzle pieces, you need to collect Enigmas (shown at the bottom of the image below) from successfully completing dates with the girls. Do keep in mind that the ranking will be reset daily at 00:00 UTC.