Relatively straightforward - you have to clear every mission in the game with an S rank on Ace difficulty, which is unlocked after beating the game on Hard difficulty.
The easiest way to get an S rank for MOST missions is to destroy every single non-TGT enemy on the playfield.
In my opinion this is one of the more difficult Ace Combat games to get S ranks in because it also prioritizes time, whereas many of the older ones focused just on the score. What it means for you is that it is sometimes not enough to just score enough points to get the S rank, you need to do so as fast as possible too.
For reference, here are my high scores and fastest completion times that got me S ranks in every mission:
Some general tips:
Importantly, restarting from checkpoints does NOT in itself affect your rank. Restarting from checkpoint not only repairs your plane, but also restores you supplies. In some mission (like 12 and 19), doing so is the easiest way to get an S rank because the missions are split into two phases without a resupply zone, and there is a good chance that you can arrive at the second stage of the mission with an insufficient supply or armaments. Checkpoints are usually granted after an in-mission cutscene. However, keep in mind that the mission time still adds up even if you restarted from a checkpoint.
Learn to prioritize targets - enemy planes yield more points that ground targets. One mid-to-high level enemy plane like an Su-33 or an F/A-18 can be worth as much as 4 or 5 AA guns or tanks.
Make an effort to seek out and destroy Ace airplanes - those are worth around 1500 points each, more than almost any other target in the game, but are not much harder to shoot down than a regular drone or plane. Refer to the guide linked in this solution to see how to spawn Ace enemies
Don't just spam missiles once you get a lock. You want to spend as little time on every enemy as possible. Take an effort to line yourself up so as to not have to do a second run. When facing ground targets remember that every target APART from tanks only requires 1 missile to destroy. If you are quick, line yourself up correctly, and make use of your machine gun, one strafing run can take up 3-5 ground targets.
Same with drones - every non-boss drone in the game (actual drones, either the MQ-101 or MQ-99, not remote controlled planes) ONLY REQUIRES 1 MISSILE TO SHOOT DOWN. Many people get in the habit of automatically double-tapping all targets once they get a lock. In the cases of drones and most ground targets that's wasting time and missiles that can be used elsewhere.
Load-out wise you obviously want to stick with the hi-end planes as much as possible. I wouldn't recommend using the X-02 because of its lackluster special weapons.
In terms of parts, I would advise you forego any updates to your machine gun or missile power (for most enemies it does very little to actually change the number of missiles required to down them) and instead focus on boosting the speed, homing ability, and distance (preferably in this order) of your primary and special weapons. Specifically for mission 9 you want to have both the Bulletproof Fueltank AND the Automatic Fire Extinguisher.
I used an SU-57 with a PLSL for most of the missions. PLSL is an excellent special weapon that I probably used more than my missiles. It is basically a dual-laser canon. If you flew fighters in Battlefield V or SWBF2 this will feel somewhat similar. With the right upgrades and as long as you can lead the shots right, it can hit targets at way over 7Kms away, further than almost any missile.
Personally, I found missions 9 (Faceless Soldier), 12 (Stonehenge Defensive), 13 (Bunker Buster), 19 (Lighthouse), and 20 (Dark Blue) to be the most challenging in terms of getting an S rank, so I included some pointers for those particular ones.
In Mission 9
In Mission 12