*Please note that this solution contains Very Minor Spoilers*
For efficiency, its best to use an Engineer class to complete Overload, Neural Shock, AI Hacking, Damping, and Sabotage on one character. However, for this trophy, you can also use an Infiltrator and Sentinel class. Overload requires at least 1 point in the Electronics skill. A Sentinel must unlock this skill after putting 4 points in the Decryption skill (5 total).
Important: This trophy does not require a target. It can be cast on anything, anywhere.
The easiest way to obtain this trophy is to cast the skill whenever it's available, even if you don't have a target. You can do this while walking around the Citadel. Just wait for it to recharge and cast again. Additionally, if you have a few extra skill points, put them in your class skill to somewhat reduce recharge time.
Final note: Only Neural Shock and AI Hacking require specific targets. Other Engineer skills can be cast into the wall/ground/air.