I agree with Fallimar, latex is hard to work with, hard to wear (though it has its pleasures ...

) and costly, I speak from experience.I went on a latex making course last year (in London)) and have since made a couple of clubbing outfits and a cosplay (Pyslocke
http://www.therpf.com/showthread.php?t=231552 ) . All my latex outfits are rather simple but took multiple attempts to get anywhere near right.
As mentioned above, you don't sew it, you glue it (You need rather specialised adhesive and thinner too) with overlapping seams, straight seams are fairly easy once you habe the basic technique, but curved 3d ones take quite a bit of practice to do neatly. You can also do appliques fairly easily by glueing on patches but its easy to make a mess with excess glue. Latex can be printed on but I think it requires rather specialised equipment.
That Andromeda Latex
http://andromeda-latex.com/ (They renamed themselves from anatomic latex) one is spectacular and must of taken an age to make by a very experienced latex fabricator and cost a fortune (I believe it was a one off, they don't sell it like there other suits) . I think its a mixture of glued sheets, moulded sections, appliques and printed sections, all made to measure for the model (Latex doesn't stretch as much as you think, skin tight bodysuits have to be made to measure)
So while latex would be possible, it would be long hard work skilling up and rather costly (Latex sheet doesn't come cheap).
I think a Lycra/Spandex suit would be a lot easier and cheaper and far more comfortable to wear, most EDI cosplays I've seen went this route. You can get very shiny metallic (actually its a thin PVC coating on the fabric) spandex quite easily at fabric shops and sew that up perhaps with black glossy lycra/spandex sections for the main body of the suit, then paint and/or applique sections for the details?
Possibly another way would be Dye Sub, paint EDI flattened out in photoshop over a base female template (people sell these I think) , perhaps even get the EDI texture (I think people have ripped it from the game) to help, then have it printed on white spandex by a fabric on demand service and then sew it up as a catsuit. Or perhaps use a mix of Dye sub and sewn sections? I think this
http://inatimeofcosplay.blogspot.co.uk/2014/05/costume-edi-15.html one was done that way