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:
*** Spoiler - click to reveal ***1) Mission 1: Charge Assault
Score: 12620, Time: 05'09''39
2) Mission 2: Charge the Enemy
Score: 10560, Time: 05'54''89
3) Mission 3: Two-pronged Strategy
Score: 19440, Time: 09'54''35
4) Mission 4: Rescue
Score: 20250, Time: 09'51''92
5) Mission 5: 444
Score: 21,920, Time: 07'24''61
6) Mission 6: Long Day
Score: 33570, Time: 15'00'00*
7) Mission 7: First Contact
Score: 9100, Time: 10'53''82
8) Mission 8: Pipeline Destruction
Score: 35970, Time: 11'48''10
9) Mission 9: Faceless Soldier
Score: 16300, Time: 09'19''47
10) Mission 10: Transfer Orders
Score: 12120, Time: 10'31''01
11) Mission 11: Fleet Destruction
Score: 48590, Time: 15'00''00*
12) Mission 12: Stonehenge Defensive
Score: 44850, Time: 15'31''00
13) Mission 13: Bunker Buster
Score: 26140, Time: 08'05''05
14) Mission 14: Cape Rainy Assault
Score: 19590, Time: 07'14''97
15) Mission 15: Battle for Farbanti
Score: 50400, Time: 21'32''51
16) Mission 16: Last Hope
Score: 24540, Time: 18'34''27
17) Mission 17: Homeward
Score: 28630, Time: 14'32''44
18) Mission 18: Lost Kingdom
Score: 15140, Time: 11'00''38
19) Mission 19: Lighthouse
Score: 57300, Time: 19'59''54
20) Mission 20: Dark Blue
Score: 12350, Time: 09'58''41
* these missions go on for a set amount of time so you only need to worry about destroying as many hostiles as possible within that limit
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
*** Spoiler - click to reveal ***it is imperative that you prioritize time. This is the only mission for which I didn't use an Su-57 with PLSL, and opted for an F-35 with 8AGMs. As I've mentioned before, whatever plane you choose, make sure you get the Bulletproof Fueltank AND the Automatic Fire Extinguisher. You might also want to invest in an increase payload of special weapons. The mission is split into two parts. In the first one you are tasked with destroying radars that guide missiles that force you to stay under the cloud cover, and in the second one you face off against an enemy squadron. The second part of the mission has a preset amount of points that you can earn, as there are only TGT hostiles on the playfield that you have to destroy to finish the mission. Therefore, you need to focus on the first part. For this I recommend you select a plane which can fit either the 8AGM, LAGM, or LACM ground weapons, like an F-35 or an Su-30SM as those strike targets directly from above (as opposed to just flying in a straight line) and can clear hills and mountains if you fire them at the correct angle. Don't be afraid of flying over the clouds to shoot down helicopters or mountain-top AA guns. With the mods I recommended you can survive two missile strikes and you health will regenerate back to 50% over time. Ideally you want to have more than 9000 points with OVER 7 minutes of time remaining by the time you finish the first phase of the mission.
In Mission 12
*** Spoiler - click to reveal ***make sure you don't let Stonehenge defenders get overrun or allow bombers to reach it. Also don't bother conserving ammo in the first phase and destroy as many enemies as possible. Once the mid-mission cutscene plays you will get a checkpoint -- reload the checkpoint as soon as the gameplay restarts and just proceed as normal with a fully restocked ammo supply
Mission 13
*** Spoiler - click to reveal *** make sure that you don't dawdle around. Ideally you would have around 2 minutes left on the clock and around 20500-21000 points by the time second phase starts. Cruise missiles speed up as you get closer, so you have some time to shoot down the Ace before going after them. All the same invest in a fast plane with mods that will increase the range of your weapons to make things easier
Mission 19
*** Spoiler - click to reveal ***relatively easy as long as you remember to RESTART AT THE CHECKPOINT immediately after the Arsenal Bird appears to replenish you weapons. After that you want to firstly destroy all the drones and the remaining planes, and slowly pick Arsenal bird apart, but destroying first the missile launcher on top of its wings (fly right behind it, matching its speed. You might have to destroy some of the propellers to get to the last few launchers), then the pulse launchers on the undersides of the wings (shoot from below to hit them), and, lastly, the laser (shoot from below, coming in from the front), before taking out the propellers and the remaining TGTs.
Mission 20
*** Spoiler - click to reveal ***You want to destroy all the drones (meaning both the main two drones and the Weapon UAVs AND the smaller drone that appears afterwards) with more than 19 minutes left on the clock (though some people have had luck with over 17 minutes left over at that stage). I strongly suggest you invest in missile speed, homing ability, and distance for this one. Don't bother with damage or increased payload. Don't spam missiles, wait for an opening (usually when the drones are flying directly from or at you). The PLSL also works quite well if you are good with it, but requires quite a lot of hits.