If memory serves (sorry, don't have the source), Phil Bourassa (the artist who designed Dick Grayson first as Robin and then Nightwing for the show) said that he wanted to capture a more realistic look for Nightwing, while still maintaining the classic silhouette and still allowing for the acrobatics essential to the character.
With that in mind, and by looking at the line definition of the costume, we can sort of infer as to what the costume is made of. Here's my estimates:
The overall body is some sort of durable but flexible padding, that is thinner at the light grey areas. I say thinner because they are all key flex points that would have to allow easy movement during combat (especially with acrobatics), i.e. knee and elbow joints, abdominals, below the chin to allow for ducking, and a thin line between the pads on the thighs to allow a little give as the leg muscles flex. The shoulders, fronts of the knees, and backs of the elbows look to have their own individual pad protection, likely thicker than others given that those tend to be high-impact areas during hand-to-hand combat. Finally, you have the gloves, boots, and belt that are all independent of the body suit.
To build this, I would find a fairly cheap, dark grey (or all black, since it'll be more common) neoprene wetsuit (or wetsuit liner). The neoprene is a bit thicker than a simple morphsuit, so the material will look a little more like the actual thing. I would simply paint the grey on the stomach and neck. I would use craft foam for the elbows, shoulders, and kneecaps. Then for the black lines on the suit, I would use some sort of shiny gloss paint, or sew thin black piping, to make the black definition lines on torso and lower legs (either one would give visual definition, even on the all-black suit). Gloves would probably have to be a modification of an existing pair, mask would have to be custom, and the boots look exactly like diving or snorkle boots, so you could probably just find a cheap pair of those.