Arkham Knight HQ: Trophies
Found when you grapple up to turn off the first fan. Turn around to see it on a workbench.
In the same room, there's a locked door by the generator. Use the Remote Hacking Device to open it, revealing a Riddler puzzle. This one's not too bad. Hit the generator with the Remote Electrical Charge to send a spark moving through the tubes. You'll then have to hit the switch to adjust the green tubes (you can use the Charge for that too), guiding the spark to the trophy cage. Once it pops, you can grab it with the Batclaw.
This puzzle will appear across the fan blades upon returning later in the game. Hitting the switch in the middle causes a cursor to move around the monitors; you want to time your throw to make it line up with the Riddler symbol. Do this three times to free the trophy.
This puzzle will also appear when you return. Lower the Batmobile over the pressure pad to start the puzzle up, then use your guns to hit the switches and raise the bumpers, allowing the balls to roll to the bottom. After sending one down, you'll have to time your shots to guide two down in the same passing.
This puzzle appears atop the lower blade when you return. It's pretty easy: you can use the Remote Hacking Device to make the cogs rotate, and the Riddler switch changes the direction of rotation. Guide the trophy ball to bottom - taking care not to dump it over the sides - to pick it up.
Found in the elevator shaft of the first elevator - it makes more sense to get it now. Step out on Level 04, send the elevator up another floor, and drop down to grab it.
When you leave the fan chamber, you'll spot a Riddler puzzle on the other side of a gate. To reach it, look for a vent just over the nearby alcove. It's an easy one to solve: just use varying pulses from the Remote Electrical Charge to guide the trophy ball to the prize slot.
When you step onto the second elevator, send it up to find a cracked wall. Blow through with Explosive Gel to find a trophy on the other side.
Immediately on the other side of the elevator door when you reach Level 05. Crawl through the vent above to get to it. It's a simple on to solve: just use varying pulses on the Remote Electrical Charge to guide the trophy to the prize hole.
Sitting atop the marquis in the same room.
This one shows up by the sentry gun if you return the area later in the game. Step onto the pressure pad to open the vent, use the Remote Hacking Device to shut off the gun temporarily, then quickly send a Remote Controlled Batarang through the vent to hit a switch at the far end. This will open a grate inside, letting you send a second Batarang through an electrical current that can be used to strike a circuit board in the same room as the turret. This will open the way, allowing you to grab the trophy and permanently disable the annoying gun.