Might be bugged - didn't unlock for me when it should have done unfortunately:
http://steamcommunity.com/app/394310/discussions/0/412449431...As for the actual task, you'll eventually meet MACK - he won't help and say you need to prove yourself. You need to do the Ivangief/Prison routes and he will help once you return. It's pretty easy (but tedious) to get the power armor parts.
The achievement *SHOULD* unlock once you have the power core for beating robodon.