To beat anyone, all you need are coins 1, 2, 3, and 3, (or any multiple of those, like 2, 4, 6, 6, or 3, 6, 9, 9) and at least one with multiplier echo; use only these coins and always keep the same multiplier.

This way you can beat anyone.

Against Shinra, all you need are 1, 2, 3, 3 coins, one of them having multiplyer echo; Just use these coins to make the number on the core sphere every round, don't mess up and you'll win! (using 2, 4, 6, 6, or 3, 6, 9, 9 is a lot faster, but these coins are typically much more dificult to get, especially at the piont of the tournament)