To unlock extras mode, beat the game. To unlock minigames mode, beat tournament mode.
Enemy Compass
If you're lost and the compass isn't helping, you should be able to find your way through the levels by simply following the trail of enemies. Continue to move towards new enemies to progress through the stage.
Get Spirit Shotgun
To get the shotgun (Yusuke's best attack), you need to beat Rando. Then you will fight Gen Kai. She has all of Yusuke's moves(including the shotgun), and is slow. After that you'll get the shotgun and go off to fight the Saint Beasts.
Beat Hiei
To beat Hiei, face the top platform and dodge his blasts. When he comes out, hit him with spirit gun. (Note: If you get hit by his blasts, you won't be able to move for a couple seconds and he will get on your platform and hit you. However, when you can move again you can hit Hiei with spirit punch.
Beat 4th Saint Beast
Here are the directions on how to beat Suzaku: First, start hitting him until he splits into 7 guys. Use shotgun until he's 1 guy again. When you have low health and energy, go to the bottom left and right of the area. You will find power-ups. Repeat. Power-ups will regenerate every few minutes.
Play As Genkai
After you defeat Toguro for the final time with Kuwabara, Rando and Suzaku fight you. After you defeat them, Tarukane will fight you. He is very easy to defeat. After you defeat him, you can play as Genkai in tournament mode.