Take the Eastern door and reach the Basement Access. Be careful here, because there will be two enemies to attack Batman here and one of them is using a shield. Just to remind you, you need to stun this enemy with your cape and double-tap the jump key/button to "trample him" and deprive him of any means of defense. After you have eliminated the guards, select the Cryptographic Sequencer from your inventory Use it on the control panel here, which will determine the password (the screenshot) and unlock access to the elevator shaft.
Jump into the shaft and land near the corridor leading up to the prison [Cell Block Access]. Follow the linear path until you reach the area with all of the cells [Holding Cells]. It is a good idea to send the fire extinguisher towards the enemies that you can see in the distance (requires using the grapple) or throw them a concussion detonator, to stun them all at once. While fighting this fight first eliminate the enemies wielding firearms, as well as those trying to pick the guns up from the ground or take one out from a locker.
After you are done fighting, go towards the Western passage and reach the Infirmary. Listen to the conversation with Alfred, and locate the wall shown in the screenshot. Spread explosive gel over the wall, detonate it and enter the Derelict Elevator Shaft.
Look up and use the hook to make it over to one of the ledges above. Now, for a change, select the grapple, target at the interactive point shown in the screenshot and extend the rope. You can now use the hook to make it onto the rope and go towards the entrance to the venting shaft. This will allow you to reach the Evidence Locker, where you will find the Disruptor lying on one of the tables.