Some ghosts must be trapped while others can be destroyed. To get this trophy you need to find one of the latter and destroy it. There are plenty of ghosts that can be destroyed throughout the game. The general rule is that floating ghosts must be trapped while ghosts running on the floor can be destroyed.
The first destroyable ghost you will bump into is the Dead Fish Flier at the Hotel Sedgewick kitchen (Replay Mission: Hotel Sedgewick / Air in the Lines). Simply use your Blast Stream until the ghost is eliminate