You unlock the Parry ability
near the end of Stage 3 Research & Development. After a brief tutorial on how to use parry, you'll move through a lobby and into a "live" combat room where you'll find one lone swordsman. He's a perfect adversary to grind out the 15 & 200 perfect parry's if you wanted to get the achievements out the way.
I found the best method was just to keep pressing
in time with the beat and in most cases his attack was parried perfectly. If you die you'll spawn outside the same room to attempt this as many times as you like. It took me a few seconds to get the 15 parries and a further 10 minutes to get the full 200.
Obviously this achievement can be done anywhere throughout the game, but this was the first ideal scenario to get it finished.
Apologies on the video quality my capture card crashed during the R&D stage