You only need to win each tournament once but some will require multiple wins to get to the next level.
The best way to get tournament points is to use the rush style and mash X to dash when the crowds wants you to evade an enemy. Just wait for the enemy to attack and mash X near them. If you can keep doing that on any enemy you'll rack up a huge amount of bonus points. There's no time limit so you can do it for ages.
If you're struggling with the last two tournaments then drop the difficulty to easy. You can put it back to whatever difficulty you want afterwards as well.