I had a very hard time beating the Sphere Break tournament. In all my searching nobody had a good guide on how to beat the tournament. There are a ton of guides for sphere break, but they are all about how to beat the game when you can set what coins you use. In the tournament you are limited. Assuming the coins you get are not random per game, this is what I did.
I had the coins 2, 3, 5, and 6.
When you face the final boss of the tournament (no spoilers) you need to utilize the echo count of using the same number of coins each round to get the sphere break (called the Coin Count Bonus). Each round you complete when using the same number of coins the multiplier increases by one, which means you get more of a bonus each round. I did it with 2 coins. The goal is to build your multiplier by using the 4 center coins as much as possible, and then once you have a high multiplier you use the outside coins to increase your score.
Core number - coins used
1 - X
2 - 5 + 3
3 - 2 + 4 / 3+3
4 - 5 + 3
5 - 6 + 4 / 6 + 9
6 - 5 + 1 / 2 + 4 / 5 + 7
7 - 5 + 2
8 - 5 + 3
9 - 6 + 3
So for 2, 4, 7, 8, 9 you can use the four center coins and build your multiplier. For 3, 5, 6 you have to use the outside coins so you are at the mercy of what is around your center coins. Each round the outside coins increase by 1 until the reach 9, and then they disappear for a couple of rounds. I did find it easier that if I was able to use an outside coin to complete my break I did, thus using them up when I had the chance. If a 1 comes up your streak will be broken, so unless you were very high in your multiplier you might as well quit and retry.
When I finally completed it I only got a 1 for the first round. After that I got all the numbers I needed to keep my bonus streak going and won. So there is some luck involved.