There are 8 armour reinforcements in the game. Your armour will get upgraded after you find 4 and again after you find all 8.
#1: Cell Blocks. In a room to the left of where you acquire the Batclaw. Pull down the vent on the wall to the left to access it.
#2: Administration. Use the line launcher to get to it. In the upper-left area of the room where you had to save 2 librarians from 2 armed thugs.
#3: Administration. Under the room where you had to pop 4 sets of Joker balloons in order to open up the Joker present. Pull down a vent with the Batclaw to access it.
#4: Administration. In the entrance of the building (the room to the left of the large burning room), shock the terminal in the background to access a vent which leads you to the room containing this upgrade.
Your armour should now be upgraded.
#5: Industrial. On the other side of the fence from where you acquired the gel launcher. To access it, go to the room to the left (this is to the right of the room with the tall spiked wall and the dead engineer), and blow up the wall in the background, to then open up a vent and follow the path to retrieve this upgrade.
#6: Cell Blocks. After acquiring the gel launcher, in the hallway in the background behind the large crates (which you can pull down with the Batclaw by the way), scan and blow-up the ceiling. This is in the hallway just before the laser barrier encrypted with an Alpha security panel.
#7: Industrial. Shortly after entering the facility, after acquiring the glue gel, jam the two fans in the wall, then burst the panels.
#8: Industrial. After acquiring the glue gel, go in the sewers towards the warden's office secret entrance, but go all the way to the left (before you enter the vent). Block the downpour of water with the glue gel, then scan and blow-up the wall to the left.
Your armour should now be upgraded once more.