*Please note that this solution contains Very Minor Spoilers*
For efficiency, its best to use an Engineer class to complete Neural Shock, AI Hacking, Overload, Sabotage, and Damping on one character. However, for this trophy, you can also use a Sentinel class. Neural Shock requires at least 1 point in the Medicine skill, which unlocks after putting 5 points in the First Aid skill (6 total).
Important: This trophy requires an Organic target, or the Mako. Since using the Mako requires visiting a random planet, it will take longer to get this trophy if you choose that route.
Near the beginning of the game, once you reach the Citadel, there are a few missions you must complete before you can leave. Without giving too many details, there's one point where you are forced to go to Chora's Den and engage in a firefight. All enemies here are organic, but at least one is Krogan. If you lure him close to the main door, but then step outside, he will stop pursuing you. From outside lean against the wall for cover (though not needed, I found this helps prevent the Krogan's pursuit and keep his bullets from hitting), and then use Neural Shock on him. Even on Casual (Easy difficulty), one hit won't kill him, and by the time the skill recharges, he'll have regenerated his health. Do this 75 times and the trophy is yours. Additionally, if you have a few extra skill points, put them in your class skill to somewhat reduce recharge time (which will save about 10 minutes overall).
The Mako is simpler than the above method, but requires more story progression to utilize. Just land on any unexplored planet, get out of the Mako and save. From here you can cast Neural Shock and either wait for the skill to recharge, or reload your save and cast again. If you have Auto save turned off, the second method is faster.
Final note: Only Neural Shock and AI Hacking require specific targets. Other Engineer skills can be cast into the wall/ground/air.