Ground Zero
Clue #1: Portion of a metal bracelet
Early in Cell Blocks, you'll use a vent to crawl past a stack of crates. Exit through the vent inside this tunnel (not the left exit), and you'll come to a courtyard with several thugs and an improvised bomb. Detonate the bomb with the Crypto Sequencer, then drop into the pit to find this clue on the ground.
Clue #2: Burned needle nose pliers
After receiving the Batclaw, you'll backtrack on your way to the exercise yard. When you reach the room where you dropped the elevator with frayed cables, leap over the flames on the lowest floor. Pull the vent with the Batclaw, then crawl into another room where this clue sits on a shelf.
Clue #3: Rubble fragments
When you return to the area where Catwoman sent you on a detour, you'll use the Batclaw to rip away a vent cover. Enter that vent and crawl forward, but stop before exiting. Those little bits of rocks in front of you are actually another clue.
Thanks to commenter leonardo-sensui for tipping us off to this one!
The Joker Is Wild
Clue #1: Dead guard
You'll find this on the guard's body as soon as you enter Administration.
Clue #2: Odd assemblage of metal parts
When you ascend the shaft with the first Joker thug, continue to the top. Use the Batarang to knock away the trap door, then grapple to an upper room. In here, grapple to the ledge, then turn around and jump across the gap. Blow this wall with the Gel Launcher to find a clue on a box inside.
Clue #3: Police-issue gas mask
After opening the Joker's present, drop into the grate it was covering. When you emerge from the shaft, the clue will be on your left.
Clue #4: Spray food cans
When you enter the admin basement, use the Gel Launcher to destroy the broken brick wall above the leaking pipe. Continue through the room and take out the huge group of thugs. Grapple to the yellow ledge, shimmy right, and drop down onto the catwalk. From here, use the Line Launcher to enter the area where you blew away the brick. The clue is back here.
Kidnapped
Clue #1: Glass eye
On your way to the construction area of Administration, you'll pull a book to move a bookshelf. This is in the safe behind it.
Clue #2: Class ring
Immediately after acquiring the Line Launcher, you'll zip over an electrified floor. Drop through the hole in the floor on the other side, and the clue will be on a box to your right.
Clue #3: Hand-drawn map of Administration
When you enter from the roof (after the battle with Deadshot), look to the boxes on your left for another clue.
Clue #4: Deceased assistant warden
Just before entering the admin basement, you'll open a beta lock with the Crypto Sequencer. On the other side is a dead employee - the next clue.
