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Final Fantasy I expected players to head towards the Earth Cave and hunt down the first major boss once the game's third or so Broken Bridge is dealt with, opening up the whole sea to sail in. One can instead use this newfound freedom to seek out Crescent Lake, and the town where you'll get yet another exploration item once you've defeated the fiend of earth. While you can't get the canoe until after dealing with the Earth Cave, you can still take advantage of the slightly better equipment in the shops. A second example occurs afterward once you obtain said canoe. Instead of using it to reach the volcano where the next fiend resides, you can attempt to get though the Ice Cave first, getting the airship and opening up pretty much the entire game world. You can also use the canoe to skip straight to the Castle of Ordeals and get a few good magic items there, and the item that'll let you class change once the airship is available.
The Peninsula Of Powerleveling northeast of Pravoka (the second town). At the top, one encounters enemies from around Lefein, a town normally inaccessible without the airship. With gear from Elfland (silver sword or fire 2), many of them can be beaten even at low level, resulting in massive exp and gold.
One of the hallways on the first floor of the earth cave has a very high encounter rate. The only enemies one can encounter in this hallway are giants, which offer a better reward (and greater challenge) than other enemies in the region.
Final Fantasy II
Final Fantasy II offered a Disc One Nuke in the form of the Captains, enemies which show up as mid-late-game mooks, stationed at Fynn throughout most of the game. Once Minwu was acquired, crafty players could down Captains with liberal application of offensive magic and receive the Flame Bow, which applies Fire effects to physical attacks, and the Toad Tome, which could effectively one-hit kill nearly anything in the rest of the game, including some bosses, and with a little abuse of the game system, even the final boss.
The area to the west of Fynn has enemies somewhat more powerful than one should be fighting at that stage in the game. They drop many items, mostly spell tomes, which can be used or sold at a premium.
There is a peninsula immediately south of Altair with enemies from the Mysidia region, near the end of the game.
Speaking of Mysidia, once the canoe is acquired, a crafty player could make their way there by going south from the Altair region.. This usually required exploiting tricks to avoid enemy encounters, but allowed powerful enemies with excellent drops, and a town stuffed full of end-game equipment to buy.
Final Fantasy III
In Final Fantasy III (at least in the NES Version) it's possible to get the very best Gear after you arrive at the first village in the game. The glitch required to abuse is rather tedious, but even getting the best gear for just one of your four characters makes the whole game incredibly easy to finish.
Final Fantasy IV: The After Years
In Final Fantasy IV The After Years, Bio. In any party with a Black Magic spellcaster, this one spell is instant death for enemy parties. Why? Well, for one thing, it's literally instant—unlike every other spell in the game, it has no casting time. For another, it's stronger than the mid-level elemental spells, which are all most of your casters will have access to during their chapters (only Golbez and Fusoya have access to the best elemental spells initially). It's non-elemental, so nothing resists or absorbs it, and as an added bonus, it inflicts Sap, which most enemies and some bosses aren't immune to. (It's less this in the original Final Fantasy IV, where access to it is fairly limited before the -ga spells become available.)
Final Fantasy V
In Final Fantasy V there are multiple such things. First is the blue magic Death Claw, which lowers an enemy's HP to a single digit and paralyzes it. Many bosses aren't immune to it, and that spell can be learned from two fairly early bosses.
Also from Blue Magic is the spell Level 5 Death. This spell instantly kills anything with a level divisible by 5, which allows you to bypass a number of otherwise annoying enemies, easily grind job points at a higher rate than anywhere else outside The Very Definitely Final Dungeon as early as the start of act 2, and (if you have another Blue Mage with the level-halving Dark Spark spell) defeat one of the most difficult story bosses in the game in a single turn.
Then there's the Barehanded ability. This Level 2 skill from the Monk class gives any class who equips it the power of a Monk when fighting unarmed. Give this to your mage, and suddenly the wizards aren't squishy no more.
Final Fantasy VI
Gau is a character built around the concept of a Disc One Nuke. He mimics the attack of monsters, letting him use level two magic long before your other party members even begin to learn first level magic, and from there until the second half of the game can usually consistently stay one-step ahead of the abilities of the rest of the party. The only catch is the game doesn't tell you which monsters teach him which attacks, and finding a specific monster to teach him a specific attack can take hours.
Edgar joins the party with the Auto-Crossbow, which lets him attack all enemies at once, doing more damage than a normal attack and ignoring row. Once Edgar joins pretty much every random encounter up until Zozo can be ended in a single round. His Flash tool does even more than the Auto-Crossbow to most groups around the time the damage of Auto-Crossbow starts evening out, and the Drill and Chainsaw tools tend to deal massive single target damage.
Fittingly, Edgar's brother, Sabin, also has the potential to be this as soon as he learns Phoenix Rising. Similar to the Auto-Crossbow, it's a mostly free nuke, an easy Blitz combo to input, that hits all enemies at once ignoring row, deals more damage than a standard attack, and deals fire elemental damage. His single target Blitz techniques can be this, too. Having Edgar and Sabin in the same party can easily carry you through every random battle up to and even past Zozo with relative ease.
In the very beginning, when the Moogles help Locke rescue Terra in the caves of Narshe, you can unequip Mog for some decent equipment that will last you through a fair bit of the early game. (He doesn't need the equipment for his boss battle since dancing has the potential to end it in one round.)
The Fixed Dice are something of a Disc Two nuke. Immediately after getting the airship in the ruined world, your 3-4 person party can sprint into Kefka's tower and get this incredibly powerful weapon, assuming they don't randomly encounter any enemies that can't be run away from. Doing so makes Setzer your most powerful fighter pretty much until you decide to do Kefka's tower (the final dungeon) for real.
You can also get Mog from Narshe first and do the raid without any random encounter risks since you get his Moogle Charm which has the "No Encounters" power. This is still practically in the beginning of World of Ruin.
Final Fantasy VII
The Enemy Skill materia is this, in general. If you know what you're doing, you can get three powerful attacks (Beta, Trine, and Aqualung), the best defense spell in the game (Big Guard), and one of the best healing spells in the game (White Winds) — all before the end of the first disc.
Getting Beta from the Zolom is easy, and can be done as soon as you reach the swamp. Elemental + Fire Materia on the armor, put everyone in the back row, give everyone the Sadness status with Tranquilizers, then Poison the Zolom to add damage and he'll be chucking Beta in no time. Some luck is involved in not having the character with the Enemy Skill Materia get tail-whipped out of the fight, but you can just revive and try again. Once Beta is learned, throw it right back at the Zolom to finish it off and proceed to nuke that first disc.
You can get the Big Guard (aka Mighty Guard) Enemy Skill, the best defensive spell in the game, from the enemies along the beach near Costa del Sol. It puts Haste, Barrier, and Magic Barrier on your entire team in a single action, and much earlier than the Time and Barrier materias become available. Plus it saves you the necessary level grinding to get those materia up to par.
As soon as you get the buggy, drive around in the desert until you encounter a Harpy, and learn Aqualung from them. You might need Mighty Guard to survive it, but that's no problem, since the Beach Plugs on the nearby beaches know it. Aqualung will kill practically every mob in a single shot from there to the end o disc one.
The Chocobuckle enemy skill from wild chocobos counts, if you're playing the original Japanese version. It's obtained about the same time Beta becomes available, and costs only 3 MP. It deals damage is equal to the number of times you've run from battle multiplied by the caster's level, so by escaping 100 times or so, you can easily be doing four-digit damage before you reach Junon. Being a Game Breaker, later releases nerfed it to only deal damage damage equal to the number of times escaped (which makes it virtually worthless).
Even the basic Matra Magic enemy skill, the first skill you can acquire seconds after stepping out of Midgar, qualifies in terms of how big a leg up it gives your spellcasting characters. Normal spells can only target all enemies at once by linking them with All Materia, and even then only as many times per battle as the Materia's level. Matra Magic, along with Beta, Trine, and most of the other Disc One Nuke enemy skills, targets all enemies at once every time it's cast, which is a massive advantage against large enemy groups. White Wind and Mighty Guard, similarly, will target the whole party at once and thus save large amounts of casting time, but the advantage Enemy Skill has over normal magic is evident from the very first skill you can acquire with it.
Gaining your first level 2 or 3 Limit Break is a matter of how many times that character has dealt the killing blow to an enemy. Gaining the second one at each level just requires using the first one a certain number of times. It takes about 300 kills for each character to gain their first level 3 Limit Break, which can be done very early in the game with a little effort. These are almost all gamebreakers, to varying degrees.
Barret and Cloud's level 3 limit breaks can be obtained in the starting area. It's just a matter of patience. The infinite parade of soldiers will drop enough potions to keep your HP up.
Cloud's 3/1 limit break, Meteorain, fires 6 shots at random targets, each doing 1.5x his normal attack damage. While this is powerful against a group of mooks, it's utterly catastrophic when you're only fighting one enemy, such as a boss, and all six shots are guaranteed to target him. Even the "hard" disc 1 bosses like Lost Number and Demon's Gate can go down in one hit!
Aeris' 3/1 limit break, Planet Protector, makes the party invincible for a short time. This can assist greatly in gaining the aforementioned game-breaking enemy skills, as well as being powerful in its own right against boss monsters.
Aeris' 'Fury Brand' limit break is potentially even more powerful. It empties Aeris' limit bar and automatically fills the limit bar of the other two party members. Not only is this incredibly useful for grinding limits and putting out large amounts of damage, but if the other two party members are on their third tier of limit breaks it can be used to fill their limit gauges at an increased speed.
If you're loaded with cash, very lucky, and have the patience of a saint, you can grind through the Battle Arena and get the Omnislash item on Disc 1, just before the Temple of the Ancients. Bear in mind that you're attempting this without the Ribbon, which leaves you vulnerable to many of the Arena's more sadistic reels. The sheer irritation is enough to make it a Bragging Rights Reward as well. After the hell actually getting Omnislash entails, Level Grinding Cloud's limit so you can actually use it is paradise. Hop off in the part of the Mideel area you can reach and battle your weaselly guts out, you masochistic champion.
Final Fantasy VIII
Creative use of the card game and a card-to-item converting ability (along with various item-to-item converters and item-to-spell converters) could get you most of the powerful spells and even the ultimate weapons before the end of disk one; using the 'Card' ability to turn monsters into cards also counts, but you probably won't be meeting anything worthwhile at that point. This, though, literally takes hours, almost as long as it would take to get them "honestly". Many players did it for the pure joy of defeating even the end-of-disk boss in one move.
You can quickly grind out Siren's L-Mag RF (which barely takes twenty minutes of random battles) and spend your first couple of SeeD paychecks on Tents and Cabins, which refine into Curagas. It's really easy to have 3000+ max HP on one of your characters after the second dungeon. Then, keep your characters with 3000+ max HP in the 500-900 HP range (at least during Disc 1). This will allow them to use their Limit Break attacks frequently while still leaving them with enough life to survive most enemy attacks.
On the topic of junctions, as soon as Attack-J becomes available and spells like Death or Break can become stockable, your characters can OHKO any non-boss enemy susceptible to those spells. Since the chance of the added effect is dependent on the number of spells you have stocked, stocking 100 of each (and never casting them) translates into a Death or Petrify chance of over 90% per attack. This is extremely useful for grinding and taking out enemies that are many levels above your party. The only danger is if your characters become confused, you have a very high chance to game over.
The PC port included a separately opened mini-game (actually a port of the Japanese Pocketstation mini-game) that would play itself (though you could also play actively). If you let it run for a few days, then you'd have a buttload of items. Then you could open the main game and transfer those items, which included stuff you couldn't even find in the main game (like the Ribbon ability, and the Mog summon). And if you'd copied the savefile before transferring, you could abuse this to the absolute extreme.
With enough patience and leveling, one can gain 300 Water Spells as early as Pre-Fire Cavern to junction to Strength in Disk 1. Before the higher-end spells come into play, Water is the absolute best Damage junction available during Disk 1 and you're more than capable of killing any standard enemies you face.
Patience and leveling, no. Fish Fins, dropped from some of the first enemies encountered (Fastitocalon-F), provide 20 Water each when refined. Their cards also refine into a Water Crystal, which gives 50 more Water. The end result is that with a brief bit of work, a player need never run out of Water. And the best part is, if doing a Low Level Run - which the game actively encourages - the Card ability gives no exp...
With about three hours work, you can get Squall's second best weapon before leaving Balamb. The cards needed are all held by the more difficult card players within Garden. The other characters cant get anywhere near as huge of a boost.
It's very possible to get Squall's best weapon - as well as the Limit Break - halfway through disc one. It requires mugging specific enemies for the parts and/or farming cards, and a lot of patience (It's not that hard, but it's very time-consuming), though. The best thing about it is that once you get the Lion Heart, the game automatically adds all the other Limit Breaks to Squall's abilities.
The Fastiticalon-F enemies give decent AP and can be encountered as soon as Squall has access to the world map. With a bit of patience, it's possible to learn all of Quezacotl's Summon Magic+ skills (alternate way is to play cards and mod them into items that will teach it the skills instantly). Why Quezacotl? Being a Lightning-elemental, it's particularly good at causing big damage against the rampaging spider-bot during the escape from Dollet. If you bring the boss to zero HP, you're rewarded with a whopping 50 AP. It's quite possible to fight it repeatedly and rack up around 400 AP, thus mastering many of the skills your current Guardian Forces possess.
As soon as you gain the ability to pilot Balamb Garden around the world map, you can fly to the Centra continent and follow the eastern side until you reach a small mountain pass that can only be entered by exiting the Garden and going by foot. If you head all the way to the end of the desert region (Kashkabald Desert), you should see a small island that cannot be accessed at this time. However, in this area you can fight Cactuars. They're very evasive and give little EXP, but are worth 20 AP each, allowing your Guardian Forces to master skills faster. If you completed the Centra Ruins and acquired Tonberry, its Call Shop, Haggle, Sell-High, and Familiar abilities can be mastered quickly and make shopping cheaper and have a better selection of items.
Final Fantasy IX
It is possible in Final Fantasy IX to net nearly every character's best or second-best weapons by abusing the Chocobo Hot-and-Cold digging side-quest. If you abuse it enough to gain the flying chocobo you can even enter other continents prematurely which causes the game to bug out and skip a large chunk of the plot. This was fixed in the greatest hits version of the game.
And another Blue Magic spell, Quina's Limit Glove, does a guaranteed 9999 damage if your HP is 1. This is still a one-hit kill on bosses well into the second disk.
This is an example of a niche spell useful for grinding a Beef Gate. The second exit from Gizamaluke's Grotto, lets you reach a forest full of Garudas, very potent birdlike monsters. Limit Glove is your only way to grind EXP from them, but if you do so, you will gain levels amazingly fast, and until Disc III life will be a cakewalk for you (unless you're forced to switch to Garnet's party, which is not high-level...)
And if you grind patiently at the earliest opportunity you can gain enough magic points for Garnet to be able to use her monster summoning abilities, a few discs before the ordeal where she actually learns to summon according to the plot.
There's a Bonus Boss in Alexandria Castle's library, Tantarian. If you beat this Boss, you will be rewarded with the Running Shoes, an accessory that teaches Auto-Haste status on your party. It's possible to fight Tantarian as early as Disc 2, although he would certainly be a challenge then.
Final Fantasy X
In Final Fantasy X, if you invest enough in O'aka's store, you can obtain several weapons with the "Stone Touch" ability as early as the Mi'ihen Highroad. It doesn't even matter whether the weapon in question is usable by a damage dealer (can be Lulu's doll or Yuna's staff). With a 30% chance to petrify virtually every non-boss enemy from that point onward, random encounters and grinding become absurdly easy.
If you're patient, by the time you leave Besaid you can abuse the sphere grid to the point where you can have Lulu and Yuna's Ga level spells which basically allows you to one shot or heal completely in every standard enemy encounter until at least half way through the game. You can also get hold of Tidus's Blitz Ace Overdrive by hitting the Besaid mooks 70 times with his regular limit breaks - something that's child's play once you replace his stoic default setting (which increases the Overdrive gauge every time he takes damage) with Warrior (which increases every time he inflicts damage.)
After leaving Besaid, your ship is attacked by Sin. It infinitely spawns Sinscales, which can be killed repeatedly to acquire a lot of Spheres, AP, and a decent chunk of Gil given enough time.
Tidus can acquire a high-tier Overdrive mode right at the very beginning of the game, "Loner". Have him KO Auron during the very first encounter with the Sinscales, as these do not attack you. Then have Tidus use Defend/Block until he learns the mode. Loner Mode boosts the Overdrive Gauge much faster than the mode you start with (Stoic). Handy for getting the Blitz Ace Overdrive mentioned above.
Final Fantasy X- 2
In Final Fantasy X-2, there is one point in the game where a merchant shows up on your home base for a while. Due to a mechanic with him alone, if you have a half-decent startup amount of cash, you can cause him to be the cheapest merchant in the game simply by buying as many Potions from him as possible and selling them back ad nauseum. This doesn't sound like much, but in his final state after doing this enough the items he sells are cheaper than he'll buy them back for. Result is instant infinite gil. The problem is that you can only do this at a specific point about halfway through the game.
Crossing over with Peninsula Of Powerleveling, there's Shell Shockers in the dry plains, accessible as soon as you get control of your Global Airship (which in this game is as soon as you finish the prologue). While their 4,700 HP is intimidating, their only attack reduces HP by a fixed percent, meaning it can't kill you, yet it still gives a ton of experience. Taking out even one of these is enough to make the first chapters noticeably easier.
Final Fantasy XII
Final Fantasy XII allows many opportunities for this, through its minor aversions of the Sorting Algorithm of Evil which place certain high-level enemies in early areas of the game. By beating up on these enemies during the time at the start of the game when the player only has Vaan, one can take advantage of Leaked Experience to power up all the other characters before even getting them. This enables a determined player to raise their characters to the levels they'd normally be at game's end in just a few hours. A bit later in the game, provided one has a strategy guide, one can enter the Necrohol of Nabudis to obtain the game's most powerful weapon about a fourth of the way through the main storyline.
The License Point system in Final Fantasy XII is a bit of a Disc One Nuke, although its effects diminish the further you go in the game. It's a board, somewhat reminiscent of FFX's sphere grid, which is filled with "licenses" for all of the game's equipment, skills, and magic, as well as a section dedicated to power ups for the character that has the license. Increased attack power, extra HP, significantly less wait time between turns, etc. The important difference between this and the sphere grid is that it isn't a straight line; as long as an adjacent square is activated, you can activate any square on the board whenever you want, provided you have the license points necessary. The game keeps you from getting any of the more powerful spells and equipment too early on, since you have to BUY them in a store as well as acquire the license, but there's no such restriction on the so-called Augment licenses. Add that on to the fact that every enemy in the game gives at least one license point, regardless level, and it is possible to grind wolves and cockatrices in the beginning of the game, and before reaching level 10, have exactly 1000 more HP than you're supposed to, have three times your base MP, cast an 8-MP spell with an actual cost of 5, and fly through many of the game's first bosses.
The powerful Quickening attacks are available as soon as you buy them from the License Board. Without too much grinding you can have all 3 Quickenings for each character before Raithwall Tomb. You can then use Quickening chains to curb-stomp bosses well into the Act 2.
With three Quickenings each, even That One Boss opponents like the Elder Wyrm and Tiamat rapidly dissolve in an orgiastic CGI display that resembles an orbital strike more than a sword fight.
Along the same lines as the Zodiac Spear is the Arcturus, the second most powerful gun in the game and achieved only through selling things to the Bazaar. You get it by selling 2 Yensa Fins (poaches from Yensas and Bull Yensas in the Yensan Sandsea), 2 Wyvern Wings (rare steal from the Wyvern Lord hunt in the Yensan Sandsea, strange since respawning enemies equals respawning loot, you can, with plenty of patience, steal dozens of wings from this one-of-a-kind, 4-winged creature...and it can still fly...), and a Salamand Halycon (rare steal from Salamand Entite in the...I'm sure you can guess where). How soon can you get all these things? About 1/8 of the way through the game, just after escaping the now-destroyed airship Leviathan and the story takes you to the Yensan Sandsea.
With a little patience and luck you can grab a Gladius, a wind-elemental dagger with a respectable 45 attack power, as soon as you enter the Giza Plain, although it's less suicidal to do it once you've acquired Basch and the Sleep spell. Sneak into the Westersand and chain 20 wolves to spawn a Lindbur Wolf. The wolf can kill a party member in one hit, but if you run back and forth between the wolf's zone and the zone next door, spamming sleep, blind and steal with each member, it's likely one of them will take and you'll snag a Gladius. This dagger is amazing, effective almost up to the Paramina Rift, relatively easy to license, and extremely fast. It's best acquired before Raithwall's tomb, as it's elementally super-effective against the Urutan-Yensa, of which you will have to kill approximately ten bajillion before you finish the Sandseas.
XII is full of opportunities to sequence break and obtain weapons and equipment that are not typically available until much later in the game. Because the game adjusts most monsters' stats relative to your level, a sufficiently powerful armor can allow characters whose level is in the single digits take virtually no damage. If they are using powerful weapons, they can deal thousands of damage as well. Powerful equipment is central to a "122333 Challenge" game, where all the characters are left at their initial levels.
Stage 2 of the Lhusu Mines, a level 35-40 area, has two chances to jump 2-5 stages above the weapons you'll likely be wielding at around that point. The Zwill Crossblade that can be dropped randomly by the Goddamned Bats is two stages above the highest dagger you likely have access to, the Orichalcum Dirk, but more impressively, a chest in the room where you kill the Antlion has a chance to contain a Fomalhaut, which lets your gunner skip the Spica, Antares and Arcturus guns entirely. Virtually every enemy between Rabanastre and Archades will then drop in one round, two if it's flying, from the Fomalhaut's 3000 HP damage output.
Final Fantasy XIII- 2
It's possible to get the Moogle Throw ability, which enables one to reach out-of-reach treasure chests, several hours before one is "supposed" to have it, which expedites sidequests significantly, gets you awesome loot, and opens up some otherwise inaccessible areas, which may be home to more nukes.
But the real nukes are the monsters in your third party member slot. With the assistance of a FAQ or guide, you can find monsters that can last you the entire game in the first area where monsters can be captured—such as the Pulsework Knight, a mighty Sentinel that allows you to survive high-level encounters at a relatively low level.
Archylte Steppe. In its entirety. It is a treasure trove. For example—the Red Chocobo and Blue Chocobo, absolutely ideal Commandos and Ravagers, can be fought and caught in Archylte. It'll take some doing, because at the first time you enter the Steppe they're Boss in Mook Clothing-level encounters, but it can be done (the aforementioned Pulsework Knight is very helpful in this). And once you've caught them, consider that due to what must have been a testing oversight, the process of getting Rare Candy to level them up with—getting the mid-tier candies is also going to net you 99 of the high-tier candies, which is more than enough to slingshot them to 99. Difficulty curve, what difficulty curve?
If you manage to max level the Dragoon from Augusta Tower 200AF, you will be able to use him through the rest of the game, short of Bonus Bosses. This is because it has ~600 Attack at a time you are at the 250s.
Snagging a Tonberry from Bresha Ruins 300 AF is very tough, but doable, and you can get into Bresha Ruins 300 AF as soon as you get your first Wild Artefact. While you will need to be powerful enough to stand up to the Tonberry's attacks, a Tonberry is an excellent Commando, much cheaper than Chichu, and with Strength and Magic approaching 1000 at max.
Lightning Returns: Final Fantasy XIII
Majority of the DLC outfits that can be bought for real money tend to become this, as you can access them as soon as you complete the tutorial and start Day 1.
Cloud's outfit (Soldier 1st Class) gave the powerful locked ability Heavy Slash Lv2 almost immediately; but it also came with the Slayer enhancement, allowing for a massive damage increase when used on a staggered opponent.
The Samurai pack, which included 6 different armors, all with locked abilities, one having Thunder Lv2 and Fire Lv2; another having Attack Lv2 and Guard Lv2. All six also came with the enhancement Critical: Regen, allowing you to access the Regen buff.
Outfits that could be accessed virtually immediately as rewards:
Mi'qote Dress - Gave the powerful 'Esuna Mediguard' and Magical Slash abilities.
Soldier of Peace - Gave access to the insanely powerful Artemis Arrows enhancement.
Midnight Mauve - A storyline garb, but one that can become extremely useful if aquired early thanks to the Fira Lv3 ability.
Any of the storyline weapons, including Caius Ballad's greatsword!Chaos' Revenge.
HARD MODE. Since all of your garbs and most of your weapons are saved over, you can start the new 'Hard Mode' game with your strongest garbs and weapons; not to mention the fact that you can upgrade your weapons and shields, in short you become much more powerful than you were compared to the start of Normal Mode. The monsters you struggled to beat first time round, or the boss that took you 12 attempts and a lot of rage to defeat, well now they have more health, but you can dish it out a lot faster, harder and better.
Final Fantasy Tactics
In the original Final Fantasy Tactics, make a character into a White Mage early on, and then use up all the Job Points you acquire to get the Holy spell. You'll generally only be able to use it once per battle because of the high MP cost, but it's pretty much guaranteed to kill whatever it hits in the early part of the game. It's great for dealing with Gafgarion after his Face-Heel Turn.
Experience points are rewarded for performing any action on friend or foe, not by defeating enemies of a certain level. For this reason, it's actually possible to reach level 99 in any single battle in the game, since each action rewards 10 experience points, and it takes 100 experience points to reach a new level. Job Points, which are used to master job classes, are gained in the same fashion, so it's also possible to master any class in a single battle.
To speed up the the exploitation of this system, there's "The Insane Frog Deathmatch". Not only is it highly effective, it's also hilarious.
Stealing Gafgarion's Blood Sword the second time you fight him will make any close-quarters fight from then until Chapter IV (including the duel with Wiegraf) a cruel joke, as it allows your strongest physical fighter (probably Ramza) to attack AND heal the same amount of damage simultaneously. With Counter or First Strike you can make someone invincible to any attack that isn't ranged or a One-Hit Kill. The problem with that is that Gafgarion is That One Boss in his own right, and getting a thief close enough to steal the Blood Sword without being killed by said Blood Sword (or frozen in place by the two nearby Time Mages, or riddled with arrows by the Archers, etc.) requires a bit of work on its own.
Making a unit a Monk and giving him/her the Knight's Equip Armor ability helps well in the early game, as the considerable boost to HP (the armor) and attack (the Monk class' properties) increases their chance of survival.
Final Fantasy Tactics Advance has the Cinquedea weapon which teaches Thieves Steal:Ability, enabling instant mastery of abilities by stealing them from enemy units (instead of careful job rearranging and sending them on about eight missions). It's a reward for reaching level 30 in the Negotiate skill, which normally will happen about 55-60% of the way through the game - however, grinding a series of repeatable dispatch missions can boost this stat without making significant game progress, meaning that you can reach level 30 and get the Cinquedea before the third storyline mission. One of the abilities which can be stolen from that mission's boss is Steal:Weapon (not normally available until around 80% progress) - and at that point, things just get psychotic.
Final Fantasy Tactics A2 nerfed many things that broke the game in Advance, but there are new nukes to abuse. Getting the ability to buy tokens in the auction houses early can let you take control of all the regions easily, and then bid on powerful items like 'Zeus Mace' or 'Excalibur'. These auction houses will actually give you even more broken rewards for sweeping the lots subsequent times.
It is also possible, by completing the right quests, to gather the trade goods needed to unlock top-end equipment for purchase, right from the get go even.
Several of the missions themselves, which were intended for mid-to-late game parties, reward powerful equips outright and can be beaten just a couple of hours into the game, by abusing skills like Mirror Items which are obtained very early with the (ab)use of the two mentioned tricks.
Among these are the 'Sequencer' sword and the 'Peytral' armor, strong items on their own right that become even more powerful each time you use a Opportunity Command in battles. With enough 'Opportunity Command' uses, the two items are effectively peerlessstat-wise.
In fact, any combination of these three examples can be (ab)used almost immediately after you start a new game.