This trophy will be earned once you've completed the main story with Terra. You'll need to beat three boss fights back-to-back. During the first fight there will be two opponents. Just focus on Vanitas and the other one leaves you alone if you don't come near it. Though don't ignore him completely, as he will launch an attack once in a while. The fight will end after you've depleted more than 1 health bar of Vanitas. Thunder Surge and Chaos Blade are effective against him. Don't spam it, because Vanitas will teleport away and attack from behind. 

The second fight is against the other boss from the previous fight. Once again, Thunder Surge and Chaos Blade work really well and can stun-lock the boss. When the boss summons a swarm of flying keyblades, use Chaos Blade to easily avoid them and damage the boss simultaneously. During the third fight the boss will be using commands that Terra can use too, like Dark Haze, Ars Solum, Quake, Curaga, and the Dark Volley shotlock. Keep your distance from the boss when he uses Ars Solum, because you'll get caught up in the combo. Use Thunder Surge when the boss attacks with Dark Volley and when he heals, as that will temporarily stagger him and you can use another surge command.