Often times you’ll run into these instances where a lockdown is initiated and the only way to exit out is to destroy the Sentry Guns in the room. Destroy one of these guns from a distance with your Blaster (the pistol with infinite ammo) and the trophy will unlock. This is also the best way to destroy them anyway as it helps you conserve ammo.
Planting your own Sentry Gun and then destroying it with your Blaster does not count. It must be one of the hostile ones. You'll run into your first enemy sentry gun shortly after escaping the air leak in Level 1. Shoot the gun from a distance with your Blaster and the trophy will unlock.