*Please note that this solution contains Very Minor Spoilers*
This trophy is only obtainable while playing as an Engineer class. AI Hacking requires at least 1 point in the Hacking skill, which unlocks after putting 7 points in Decryption (8 total).
Important: This trophy requires a Synthetic target. This includes turrets.
Using AI Hacking naturally while progressing through the first game world will put a big dent into the 75 needed casts to get this trophy as the vast majority of enemies are synthetic. However due to the requirements to unlock Hacking, a new character will definitely come up shy of the mark before reaching the Citadel. Of course through natural gameplay, AI hacking is easy to complete as there are more than enough Geth and other synthetic targets, but to speed up the process, follow these steps.
Once you reach the Citadel, progress through a few main missions. Without giving too many details, there's one point where you go to Chora's Den and confront a man named Fist. Before entering Fist's office, save your game. Command your allies to stay outside, then enter his office and take cover against the left wall. Two turrets will rise from the floor on either side of the small wall Fist hides behind. Use AI Hacking on the right turret first (or it might hit you). After the skill recharges, Hack the left turret, but be careful not to linger. Once both turrets are hacked, the game automatically progresses to a cut scene (which just wastes time before you can load again). So before this happens, reload your save and repeat these steps. Additionally, if you have a few extra skill points, put them in your class skill to somewhat reduce recharge time (this won't save much time, but also doesn't hurt).
Alternatively, you can hack either turret and then immediately reload. If you have auto save off, this would be the faster method.
*Please note that normally Fist and the left turret destroy the right turret after it's hacked, but if they don't and it kills the other turret, the game progresses to the aforementioned cut-scene, so be aware of this.
Final note: Only Neural Shock and AI Hacking require specific targets. Other Engineer skills can be cast into the wall/ground/air.