The judgement link can be initiated by pressing the A button while a monster is off guard (knocked down, attacking or has its back turned to you) to launch the monster into the air, at which point you can press the X and Y buttons to juggle them. If you use one button repeatedly, it will keep making the monster go higher, increasing the damage dealt and the items they drop, making it good for collecting Mystic Jewels and restoring MP but making it harder to keep hitting them, however if you alternate X and Y then it will keep the monster low, making it easier to hit and doing less damage, making it good for increasing your weapon levels and a monster's hit count record.