In every standard Objective Mode level, there will be special events that trigger at random while the Objective Mode timer is active.
One of these is "Kill the glowing red dots". This requires you to make your way to the marked waypoint on your HUD and swat at the glowing dot that appears. The dot will then move to a new location. Repeat 3-4 more times before the event timer runs out to complete the event (you'll get a yellow (upgrade) or purple (power up) box as a reward) and unlock this trophy.