This entire Process Falls Under:
Abusing the Forced Captain Spawn to Level all weapon proficiencies to 16, all base stats to 99 (including Agility), and to cap out any magic you have access to (which is most magic in the game if you don't mind an early game walk).

The quickest way I found to do this is one character at a time, so pick your first training slave and wipe the other characters out. This can be done before or after recruiting Minwu, minwu gives the Canoe but you can ignore training him due to the lack of a postgame in this version.

Because I forgot to mention this before: Spell Levels and Weapon Levels Cap at 16. Stats cap at 99.

1. The first step in this training is to cap out evasion ASAP. So take your first trainee and Equip a shield in their dominant hand with a weapon in their off hand and then take off all armor. Visit the first two towns and buy the weakest version of each weapon type. Now you want to level your first weapon proficiency until it is level 3 (the shield will also be 3); then swap to a new weapon type to continue since shields like getting experience even if they normally would not when you are using a weapon type you are not good with. After getting all weapon proficiencies to level 2 and/or 3 but bow your shield prof should be at 6 to 7

2. Equip the weapon type you want to cap first, go back to the starting town, and buy cure. Your next step is to attack yourself and heal yourself since the misses and difficulty you are as a target will grant experience to both until you have shield at 10 and the first weapon at 8 to 10.

3. Now for the grindiest part. Your evasion should be 99% at this point and you should have a few hundred max HP by now. Maxing agility requires high evasion and dodging many attacks, but cannot happen often at all with evasion below 90%, maxing a weapon type requires fighting an enemy who is much more powerful than the weapon you are using, and if used in off hand you will gain more experience for the weapon type alongside more strength. What you want to do here is make your way to the Captains in the Captured Kingdom (how you progress the story to begin with) and start fights with them. With high evasion they will almost never hit you with anything but bow (bow counts as a spell from enemies in this game so it cannot miss). Just attack and heal when you need to and your weapon levels and strength will rise until you hit the cap in strength, all weapons but bow, and your agility will increase beyond what it will ever hit in a normal run. In this version the Captains will also run away for some reason so do not worry about killing them; it speeds up the grind considerably. If you want you can stop here with one weapon and a shield capped and with whatever your agility is, or you can continue to do this until you have 99 agility and stop here (Each point of agility increases a few things, but most notably your evasion; which matters because as you equip heavier and heavier armor you will eventually have 0 evasion outside of the bonuses that weapon proficiency and shield proficiency provide, but that likely wont beat out the weight of your armor later on).

EDIT: I forgot to mention this the first time around but next to your evasion there should be a multiplier (X1 to X16). This is the number of attacks your evasion applies to. The Captain hits multiple times so it will still result in you getting hit when he attacks for your first few fights; the attacks just wont hit as hard. This will increase as you evade more attacks and as you fight the Captains until eventually your evasion will reach 16X99% Evasion and basically all melee attacks in the game ever will miss you almost always. I did not elaborate on this before but it was brought up in the comments and it was something I forgot to mention here. If that description was confusing an easier way to understand it is paying attention to your weapon attacks, notice how your character's accuracy multiplier is also the max amount of times your character will hit in an attack without buffs? Evasion is the inverse of that; so your opponent with 6X70% accuracy will attack 6 times with each attack (same for you with that accuracy), but an evasion of 7X60% means you will evade up to 7 hits from each incoming melee attack. Yes with the percent comparisons they may still hit a few times for small damage, but once your evasion starts to reach values like 13X99% very few enemies will ever hit you since most enemies do not attack that many times. This is also why the captain will usually still hit you at first when you start fighting them. They hit more times than you can evade from an attack. An example of this is if you had an accuracy of 7X80% and your target an evasion of 6X99% you will always hit your target at least once because when you attack them you get 7 hits compared to their 6 evades. Yes 1 hit is not going to be that much damage but it still hits.
I also explain but do not fully elaborate on how agility works, and that is mostly cause I said about everything I know about it from my years of play. That is:
1. Agility will not increase without High evasion (90% or higher yields an increase on average of 5 to 20 encounters for me against the captain)
2. Agility increases more often the higher your evasion multiplier is (16X99% is the best for agility farming and that will be reached eventually by fighting captains)
3. Agility likely wont increase throughout a playthrough without specifically grinding it with the High Evasion battle an enemy method I described, but all enemies seem to have equal odds of raising agility, so once your evasion caps on the captains you could always just nuke weaklings to raise agility, I just bunch it in with captain fights cause you will be doing a lot of that to raise everything else.
Sorry about not detailing all of that more specifically earlier; I genuinely forgot to mention the evasion multipliers because it would handle itself once you started fighting captains for a little bit and I forgot to elaborate agility more cause increasing it specifically is something I never pinned down aside from a few things I tested when I played it myself since I owned my first copy of FF2

Either of these methods can be done in either order. The steps are:

4A. Magic Maxing and Gil Farming:

4B. Agility Maxing for Bow Training:

4A: If you have not already done so, Buy Blizzard, Thunder, and Fire and then return to the captains and choose a spell for each encounter and cast it on him, then starting auto battle so the trainee casts it repeatedly. With starting gear this is the only way to kill the captains and it will level your intelligence, magic, and max MP while also seeing some gear drops like Flame Bow and Golden Armor from the Captains. Keep as much as you want but you will have to sell a lot of these to keep up with your MP consumption. You can also take any chance you want to just auto battle cure on yourself till the guy flees to cap cure, spirit, magic, and max mp. Once you reach the threshold where all of your base spells can instantly kill the captain, start instead casting them on yourself repeatedly until he flees or you need to heal, or just feel like offing the guy. This will level magic Defense and will eventually cap your spells, magic, int, spirit, and max mp stats. At this point Cottages will likely be more affordable than stays at an inn so start buying those. For this next part you will want to stock up on a very large amount of gil. Once you have enough gil or whenever you feel strong enough you will walk across the map to visit every other available town for any gear or spells you want (except one story related spell). I recommend going straight to the town of mages because they sell most of the magic in the game. enjoy buying up all of the magic you want and leveling it up in the same ways you leveled Cure and Fire/Thunder/Blizzard. Though an important note now is that one of your party members (outside of Minwu) should keep one empty spell space for a story related spell that BOTH gets stronger the higher its spell level is but also for how strong the rest of your spells are. Also make sure that at least one of your characters has toad at level 16 for another step later.

4B. Just keep doing melee fights with maximum evasion until your agility is high enough where you no longer need a shield for maximum evasion; now start by equipping the bow and training with it. This genuinely is the reason for getting high agility outside of wearing the ultimate armor and having high evasion at the same time.

EDIT: It appears the snowmobile minigame was actually not present in the Japanese exclusive Original FF2. So it is not present within this version. I will still keep it here in the guide in case they add it to the Pixel Remasters but it seems that the infinite Masamunes and Genji Armor sets from the minigame is not possible in this version.

Ultimate Gear. Progress to Snowmobile: If you went this far then may as well go all the way. With level 16 Toad you can access the toad memory minigame when in a snowmobile I have not reached that point yet to know this version's method of opening the minigame in the snowmobile so you will have to figure that out sadly. This game is how you get the ultimate armor and weapon in the game (weapon is a sword) and some items you will also never need. The minigame has 32 possible layouts and will rotate between them in a set rotation; so just record the layouts as you go and then win with the exact amount of failures needed for each reward (of which all are infinite rewards that you can get as much as you want). This can only be done with level 16 Toad; the game you open otherwise is not worth it compared to Toad.



MINOR SPOILERS AHEAD




SPOILERS




YES THIS GAME IS SUPER OLD BUT I DUNNO; MINOR SPOILERS




Ultimate Spell. Ultima: Once you make it far enough in the game Minwu will unseal ultima. You only get one tome for Ultima so use it to teach the one character you left a free slot on Ultima; then find a strong enemy and do what you did to level all other casting magic until it is level 16. This spell grows stronger from both leveling up but also from all of your other spells being a higher level; so enjoy its strength.

That is it; there ya go.

When your final fourth member joins Captains will not be available so you will just need to find a tough enemy. I personally would use Behemoths at that point in the story. This method will cap every stat and spell without fail; which the game was not balanced around so enjoy.

If the postgame is ever added you will want to do this process for Minwu and about every Fourth Party member that joins your team (yes not all of them will benefit from it at all in the postgame but I am avoiding spoilers so listing which specific fourth party members do and do not appear in the not-present-in-this-title's-postgame in this guide will not happen). Also; give the guy who gave you the snowmobile and every other following fourth member two of the strongest sword in the game before they leave your party if that ever becomes the case, since if the postgame is ever added; the snowmobile minigame will likely be present in the game as well (of which neither currently is so nothing to fret about there).

The first game I ever owned was FF1 and FF2 Dawn of souls on the GBA and I have gone out of my way to play every FF title in most ways I could afford to do so since; this includes NES FF1 and owning most FF titles on all platforms I can afford. I personally love to both challenge myself with the titles I play (I am a tryhard a lot of the time), but i also love creating a "Perfect Save" of every title I play where everything is done and all stats are maxed or Min-Maxed. This guide will create a save that falls in the "Perfect Save" category, and there really is no reason to do this to the extent listed in this guide outside of "Because you are probably like me and want all numbers to be at their caps to feel good", but I do hope you enjoy the feeling if you ever decide to dump the hours it takes to cap everything so soon into the game on every character.

Thank you for reading!