This requires a minimum of 18 missions on Hard as well as every mission on Normal completed with an S-rank.
Similar to AC:FA though, if you complete a mission with anything less than an S it counts against you. So for instance someone with every mission S-ranked on normal who has one C- or B- rank on a Hard mission will not unlock this when they S-rank their 18th mission on Hard unless they go back and re-do the one with the lower rank and bring it up.
I dunno the exact formula, but if you want this achievement as early as possible I suggest S-ranking every mission on Normal before progressing to Hard, then continuing to replay each mission on Hard until you S-rank it. I had all S-ranks on every completed mission and this unlocked after my 18th Hard mode mission.
I highly advise experimenting. The primary weapons you will be using are the EN-200 laser rifles on your arms, and either OGOTO or SIRIUS on your shoulders. However, for some missions where other sites advised me to rush through with OGOTOs I found it better to clear all the small stuff with my EN-200's first then switch to OGOTOs for only the main/big enemy. Also, when fighting fast-moving NEXTs, it's often easier to land hits with the SIRIUS cannons since they're nearly instant time-to-target whereas the OGOTOs take some time for the shot to arrive, allowing the enemy NEXT to dodge it.
Similarly, different missions have different requirements. Icebreaker Defense, for example, is strictly time based (and damage to the ship you're protecting too, but in order to complete it fast enough you by default prevent all damage). Missions where you fight enemy NEXTs are often time and damage-taken based, so you need speed while at the same time avoiding as much incoming fire as possible.
Tweak your tuning to apply to the mission you're tackling. Put points into Quick Thrust, Lock Speed, and Radar Refresh when fighting fast moving NEXTs. Quick Thrust and Lock Speed are good universally, as are EN Output and EN Capacity. Radar Refresh is really only useful against those fast moving NEXTs though, so put those points elsewhere for missions where the primary targets are slow or stationary. You can even put a few points into LOAD so that you can use smaller, more agile legs which would otherwise not give you enough LOAD capacity for your weapons' weight.
One example: on Internal Purge on Hard, another site suggests clearing the entire level with OGOTOs. I used EN-200's to clear everything except the 3 "large weapons" and the enemy NEXT at the end. For those two tasks I used SIRIUS cannons not OGOTOs, because he kept dodging my OGOTO shots. I found myself using the EN-200s to take out far more enemies than the guide on X360A suggests as they're so much more efficient and don't damage your own mech in close quarters. Also for any mission where I found that I did best with either OGOTOs or SIRIUS cannons, and wasn't going to use my EN-200s at all, I removed them to save weight and increase my agility.
Faster is better. I didn't use a slow, heavy mech for ANY mission's S-rank. The extra armor points are worthless if you're too slow to dodge much or complete the mission fast.