Sphere break is a mini game new to X-2. The game is pretty simple, you match up the numbers on coins add up to a multiple of the core sphere in the center.
It's available in chapter 2 in Luca. There you can get some coins for free by asking how to play the game. Further coins can be obtained from entering the tournament and digging in Bikanel Desert.
In chapter 3 there's a tournament, winning that will get you 4 wins and a dressphere. Then just play people in the locker room without the save sphere. I recommend to play the guy whose core sphere has a quota of 20 coins, because that's the easiest one to win.
From there the easiest way to win is to match up one entry coin (the gold ones) with one border coin (the silver ones on the edge). Doing so over and over again will net you echo bonuses and you'll meet the quota before the full number of rounds is done. Then once you win 10 the trophy will pop.