Combat Links are a core game mechanic. Once you unlock them during your first Free Day trip to the Old Schoolhouse in April, you should always keep your characters linked in battle. Every time you Unbalance an enemy, you'll be given the option to have the linked character perform a follow-up attack.
The first and most basic attack, the Assist, just requires you to press
during the cut-in. Do this 500 times, and the trophy is yours.