This suit is essentially the Blackest Night suit. When you wear it, you're invincible; you don't take any damage from anything (but you'll still die from scripted death zones such as the electrified floor in the Arkham Wing).
Here are the locations of the parts:
Blackest Night cowl: Administration. You'll need the tightrope upgrade of the line launcher to access this. It's down in the area with the only fight to get
League of Shadows in Batman: Arkham Origins Blackgate Deluxe Edition. From the walkway where that fight takes place, it's directly above it. Grapple up then use the tightrope to move up in the large opening.
Blackest Night chest: Cell Blocks. In the large room with the service elevator (where you see Penguin descend very early on), it's in the top left of the room. Grapple up on the right to reach the top right corner, then use the line launcher to get across.
Blackest Night gloves: Industrial. When you're in the process of ascending back up the shaft with the vents labelled with A, B, or C, it's just below the A vent. You'll have to scan and blow-up a portion of a large pipe to access it from the left. You can get to this area by passing through the large open rectangular room where 4 armed thugs were holding a guard hostage on a chair.
Blackest Night boots: Administration. In the room where you have to block 2 gas-dispensing vents by using the glue gel, then open the Alpha-encrypted door below. When looking at the map, this room is in the left part of Administration.
Blackest Night belt: Arkham Wing. While moving through the cells, after dropping through the electrified field, jam the fan in the wall in the background by using the glue gel, then go through and line launch across to access this final part.