The Bidding War
Clue #1: Gold coins
This is found in the Black Mask boss chamber. After defeating him, analyze the boxes in the right corner of the room.
Clue #2: Homemade paper target
After defeating Deadshot in Administration, return to the roof. Grapple to the ledge near the door, and the clue will be along the wall around the corner.
Clue #2: Handwritten IOU
After defeating the Joker, exit the room and scan the wall to find this.
Clue #4: Bearer bonds
On your way to the Arkham wing, slide down the left ladder at the base of the Penguin boss chamber. You'll find this clue on a machine below.
Clue #1: Personal journal
This is found in the library of Adminstration, but it's tough to get until you clear the room of thugs and Joker gas. When you do, you'll find it on the right side, next to the barbed wire divider.
Clue #2: Tiny key
When you enter a room with two thugs across a pit of Joker gas, use the Line Launcher to cross the gap. Take out the thugs and analyze near the bookshelf to find this.
Clue #3: Personnel file
You'll find this while deactivating the electrical charges by the warden. When you reach the room with two receptors, look to the table for it.
A Life on the Line
Clue #1: Rope noose
When you enter a room in Cell Blocks with a heavy stack of crates, you'll have to crawl through a vent. Take out the shock stick thug inside, then head through the next vent. Round the corner, then crawl through the maintenance tunnels. The clue is by the tunnel cover near the right room exit.
Clue #2: Damaged door
Once you've obtained the Batclaw, you'll pull down an improvised barrier on your way to the exercise yard. This is found immediately on the other side of the barrier.
Clue #3: Prisoner's slipper
On your way to the exercise yard, you'll use the Gel Launcher to blow through a wooden floor. After the big drop, there will be a ledge right in front of you. Grapple to it, and you'll be able to analyze the clue on a nearby beam.
Clue #4: Cut pipe
Inside Cell Blocks, you'll come to a large shower area. After blowing the vertical wall with the Gel Launcher, look for a weak spot on the ceiling. Blow through this, then grapple to the upper area to find a clue on the floor.
Clue #5: Torn guard's shirt
After exiting the showers, you'll grapple across the courtyard to a series of catwalks. Before exiting through the lower right door, grapple to the ledge above it. From here, you can grapple to some ledges in the background. Follow them to find another clue.