The ability to use Unison Attacks is unlocked at the end of the Ossa Trail section of the game. In battle you will see a bar above the character portraits. Every time a character hits an enemy, the gauge increases. When it turns red, you can use a Unison Attack.
In battle, get close to an enemy and press R3. You need to connect with this attack to actually enter the Unison Attack mode. If not, you will expend the charge but not gain any benefit.
Simply press the face buttons in any order to have your characters perform an attack. The Trophy will unlock soon after.