After reaching the place where the Trophy is hidden, it will turn out that it's behind grates #1 and the only way of reaching it is destroying the wooden wall directly above it #2.
Stand on the roof north of the Trophy #1 and glide towards the wooden wall #2.
Hitting the fragile wall will cause it to break #1. Jump down and pick up the Trophy #2.
Gadgets used: Explosive Gel, Batarang
The puzzle connected with this Trophy #1 is complicated and quite hard to complete. If you turn on Detective Mode, you should note that there are cables coming out of the cage with the collectible #2, leading to four different question marks. The idea is to turn them off within a short time interval.
Three of them can be destroyed with the Explosive Gel. Start off by finding the one south-west of the cage, on one of the lower roof parts #1 #2. Spray the Explosive Gel on the question mark but DO NOT detonate it yet.
The second one is on the same level as the cage, west of where the Trophy is hidden #1 #2.
In order to reach the third one, head north. You should find it quite far from the cage #1 #2.
After planting three charges, return to where the cage is. Stand on one of higher platforms and look at the previously ignored question mark (it's too high to spray Explosive Gel on it) #1. Start turning around towards the previously sprayed charges and successively detonate them #2. At the same time note that detonating the first charge will cause a timer to start.
Detonate all three charges and afterwards quickly throw a Batarang at the last question mark #1. If you have done everything correctly, you will be able to collect the Trophy from the cage #2.
Solving this riddle is quite hard and required you to activate three pressure plates without touching any other walls or ground. Start off on the roof of the building (standing on the pressure tower at best) directly north of the Trophy cage #1 #2.
Glide south. You need to fly towards the pressure plate on the wall of the building in the south #1. The key to success in this case is activating the plate and bouncing off the wall #2. In order to do that, you have to let go of A at the last moment and quickly press X. Of course don't forget to press A again after Batman bounces off to start gliding again.
It's important to try and bounce off the first plate at its upper part, thanks to which you will have an easier time reaching the next one. The plate is on the northern building wall #1, the one on which you began everything. Just like before, you have to let go of A at the right moment and press X #2.
Fly back south and keep in mind that the last, third pressure plate, is on the ground #1. You will probably be quite high above it, so choose the right moment to stop gliding. Collect the Trophy afterwards #2.
Gadgets used: Explosive Gel
Turn on the Detective Mode to note that the wooden obstacle can be destroyed using the Explosive Gel #1. After a successful detonation, pick up the Trophy #2.
Gadgets used: Cryptographic Sequencer
Get onto the lower part of the Church roof. Prepare the Cryptographic Sequencer and use it on the control panel beside the cage #1. Create the password ANALYTICAL #2 and collect the Trophy.
Check out the narrow alley behind the fence to find a spot where you can perform a slide #1. Get to the other side and pick up the Trophy #2.
Used skills: Dive Bomb, Shock Wave
Gadgets used: Batarang
The puzzle connected with the Trophy is quite untypical, as it requires you to hit a pressure plate with great force. Start off by heading to one of the vantage points south-east of the cage #1 #2.
Glide towards the pressure plate and soon afterwards press the right trigger to activate the Dive Bomb #1. Right after hitting the plate, press B to activate the Shock Wave. If you have done everything properly, all of the arrows should become lit #2. If only a part of them becomes activated, it means that the hit was too weak and you will have to repeat everything from the beginning (be sure that to choose a high enough starting point and keep dive bomb active long enough).
Stay on the pressure plate and throw an ordinary Batarang at the interactive question mark that should become lit #1. Afterwards you will be able to take the Trophy from the cage #2.
Gadgets used: Freeze Blast
Approach the place where the Trophy is hidden from the north. Choose the Freeze Blast and use it to seal the pipe from which steam is coming out #1. Gain momentum and perform a slide #2 to reach the secret.
Gadgets used: Cryptographic Sequencer + Cryptographic Sequencer Power Amplifier + Cryptographic Sequencer Range Amplifier
Approach the Trophy from the east. Choose the Cryptographic Sequencer and interact with the control panel on the right #1. Solve the mini-game to crack the password #2. Enter the newly unlocked area and collect the Trophy.
Gadgets used: Explosive Gel
Don't try using Batarangs here, just approach each of the three interactive question marks and spray Explosive Gel #1. Afterwards detonate all three charges at once #2 and take the Trophy from the open cage.