During the course of Chapter 4, you will eventually return to the Shinra Building and be put on duty in protecting Professor Hojo in his lab. In his lab, you will find a myriad of machines that you can interact with, some of which are related to trophies/achievements. There is a machine to the right of Hojo that you can hit a button, which does some things. Hojo mentions the button you pressed released some test sample monsters onto the lower floor. These monsters are too ferocious to be of any use, as Hojo points out he was about to get rid of them. He puts you in charge now of getting rid of the monsters.
To give some further incentive to do it, Hojo mentions that the keys to the locked cells on the previous floor are on the monsters. Also, Hojo has triggered a three-minute timer here, after which, tranquilizer gas will be released (you will fail). You will need the Steal Materia here, which you just got one from Bruno right as you were leaving the Sector 5 Slums. Make sure you equip this, as there is no other way to get the keys off of the monsters. To get this trophy/achievement, you will need to steal a key from each of the six enemies, then open each cell and loot the goodies inside, within the time limit.
When you’re ready, take the elevator down to the floor with the monsters, where you will see them all split up. Go to each monster to initiate a battle, then use Steal on it until you get the Jail Cell Key. From there, you can defeat the monster and win the battle, then move onto the next one. Note that the timer doesn’t run while you are in the middle of battle, so you don’t need to be super powerful or rush while fighting. Four of the monsters will be in the main hallway, while the last two will be in the room with the locked cells.
Once you have all six of the keys, open up each cell door one-by-one and loot the chests within them. There will be three chests in each cell and just to be on the safe side, loot the chests despite them not really containing anything of much value. Upon looting all of the chests in each of the six cells, hurry back to the Fusion Lab to finish before the timer reaches zero (you should still have plenty of time left, if you are pretty strong). If you did everything right, then you will unlock the Cell Raider trophy/achievement.