During the battle in Alter-World, various actions will raise the Break Gauge. When the gauge reaches 100%, it will enter in "overbreak state" where in the damge done will be increase.
The number of moves you have during Overbreak depends on the number of allies that are alive when you enter Overbreak. (2 moves per surviving ally and 8 moves at max)
When entering Overbreak, all party members will recover a certain amount of MP.
Requirements for building up your Break Gauge can be confirmed through the Menu in battle.