As you kill enemies, a meter in the upper-left hand corner of your screen will build up. Once the meter is filled, you'll be able to launch a Neon Singularity attack by pressing down on the d-pad. (The game will tell you that you have a Singularity ready.)
This trophy is for defeating 100 enemies in total with Neon Singularities, not in one shot. You should get this over time, especially if you're going for other trophies.
To get the trophy more quickly, save your Neon Singularity until there are many enemies around.