You need to get inside of the library where Miss Decibel is hiding. Head over to the marker on your map and you should see a snake basket that you can use the Climbing Cobra technique to get to the window. Go inside once you get there. You will first need to place the transmitters she was using on Salim's friends, which Bentley has reprogrammed with some new music.
Drop down to the bottom floor and head towards the stairs. Before you go up, there should be a hole you can crawl through in the corner with a bunch of destroyable objects. Do that and go to the end to plant the first tranmitters. Go back to the bottom of the stairs and use Climbing Cobra to climb the chain, then jump through the doorway.
You should see a chain over a pit, so quickly climb it and jump onto the platform, then use the hook to get to the other platform to plant the transmitter. Go back to the stairs and climb the chain at the top of them to get over the wall there. Go to the other end of the room and use both chains to get on top of the pile of books, where you'll find the last spot for a transmitter.
With all three in place, you'll be playing as Bentley. He needs to go to all three transmitters and hit them with darts. When you gain control, go to the marker right where you start and plant a bomb, which makes a hole in the floor. Stand on the different part of the floor and shoot a dart at the transmitter.
Bomb the door behind you to get back to the main area, then go to the top of the stairs to find a cracked wall. Take care of the scorpion nests, then blast through the next two walls. Jump on the stacks of books until you get to the third one, where you'll have a shot at the transmitter.
Go back to the main room and you'll need to toss bombs at the things in the middle of the room. Every time you blow one up, wait until Decibel returns to playing music before destroying the next one. Make your way across the platforms and into the next room. Destroy the thing like in the main room, then jump to the corner platform, where you can hit the last transmitter.
All that's left to do is climb to the top and over to the area where Miss Decibel is, then drop down and plant the bug to finish the mission.
