Ranger + Item Lore (which doubles the effectiveness of potions) + Mirror Items (which lets you use items for the opposite effect) + Hi-Potion/X-Potion = 200/400 damage, with the same accuracy as a normal physical attack. In a game where most of the enemies have less than 400 HP. Hilarity Ensues.
Note it mostly counts as a Crutch Character that happens to last until the end of the main quest. After that damage per attack starts needing to be higher than 400.
In addition, while other Game Breaker(s) from the first game were removed, it's still possible to put enemies to sleep (or better yet, Stop) to increase the hit chance of all effects to 100%. Including instant-kill abilities that normally have around 30%.
Parivir, a.k.a. Yojimbou. Remember how much of a Game BreakerDual Wielding was in the first game? It's outdated. The Parivir can simply walk up to something and hit it for double damage, for free, without having had to grind 999 AP. The other similar free abilities have half accuracy; the Parivir's don't. And he has multiple skills to do it with, each carrying a different element and different ailments.
Adding the passive skill Geomancy lets you also strike enemies neutral to any of the available elements (e.g. almost any enemy in the entire game) as if they were weak to the element used, bringing the damage up to triple of your standard attack. Still for free, at full accuracy, and causing a status.
Also, there exists the Hume Illusionist/Seer combo. Magick Frenzy, surprisingly, works with Illusion spells. Meaning that the unit can stand in one spot, hit all enemies with the Illusion spell, then smack all the enemies upside the head with his equipped weapon (even more so if he's using Dual Wield, although you'll have to compensate Half MP for dual wield). To prevent total abuse, while Nu Mou can also be Illusionists, only Humes can use the Seer job.
Geomancy is arguably a better support ability for the Illusionist/Seer combo, Recharge/Ether Shot/Elemental Rend MP makes half MP unnecessary and Dual Wield takes time to master in a class with relatively low Magic growth not to mention that the weapon damage in minor compared to the Illusion.
Dual-wielding weapons makes the Magick Frenzy effect ridiculous in itself when you have a physically-based class using High Magick abilities, allowing you to strike multiple foes in an area of effect with your two blades. From a distance. Add in the random chance that you can dish out critical hits with the physical attacks provided by Magick Frenzy, and it gets completely crazy even if the unit's low Magick damage makes the damage from the spell itself negligible.
As a bonus: You can equip weapons that deal elemental damage, equip your caster and their clanmates with gear that absorbs that element, and use Magick Frenzy to cast healing spells as well as damage spells. Fun fact: You can actually Magick Frenzy when casting Recharge (which restores 24 MP to the casting unit), allowing it to restore some HP along with the MP if you absorb the element your weapon deals damage with. The animation for this is amusing: The unit goes through the Restore animation, then disappears, reappears on the spot, hits itself in the face, and does the little cheering animation for receiving healing.
Elemental Rend MP. Arming a Dragoon (or Templar) with Arts of War and an elemental Lance lets him "Reverse" Rend MP two mages wearing the appropriate absorbing robes for massive amounts of mana. THIS is how you spam Geomancy-powered Illusions.
A less extreme version: an Hume Fighter with an elemental blade and Soldier moveset as an extra command. It's less intense, but in some team builds it may be more practical with only one target in need of MP and can also lead to a faster and stronger MP feeder (due to Ninja levels and Dual Wielding if the player is so inclined to train a feeder that much)
The MP system of this game means that the Blue Magick "Matra Magick" (which switches MP and HP values) can reduce an enemy with several hundred hit points to death if used early enough in the battle. Used with the Reverse Rend MP trick (or a White Chocobo Rider's Choco Recharge) this can make situations that pit the player against one or two extremely powerful enemies much easier.
Though it may not be on the same level as the other combos, the Viera Summoner/Red Mage deserves a mention. Combine Summons (powerful wide area magick), Red Magic (for Doublecast), and the support ability "Blood Price" (Cast From HP), and you've got a caster that can quickly tear enemies to shreds or heal, buff, and revive all of your units at once right off the bat. That the Summoner job offers the best Magick stat growth among Viera jobs is just icing on the cake. It does take a while to set this combo up though.
For giggles, give her the Chameleon Robe (Absorb Holy). As long as she's in range, the Summoner can spam Doublecasted Maduin (extremely high Holy damage) for free in a wide area. It is extremely overwhelming.
Forget Doublecast. Assassin + Seventh Heaven (Bow) + Summoning Magick + Blood Price = Swiss Army Knife character. Need to kill someone? Ultima Shot them from afar! Need to heal yourself and your entire dead party? Cast Phoenix for essentially no charge! Once you have the setup, those two moves will get you through the entire game.
As noted above, the Ultima skills, with a 32 MP cost, usually fall under Awesome, but Impractical. However, the support ability "Halve MP" (available to Bangaa, Hume, Nu Mou, and Viera) + the MP Channeling (double MP regen) Clan Privilege + any job that uses ranged weapons = deal 300-500 points of damage every turn at any distance. Like the Double Casting Blood Price Summoner above, this takes a long time to set up, since the Ultima skills have a 990 AP cost and Halve MP has a 400 AP cost.
The best class for this is the Bangaa's Trickster: now that Ultima is a VERY powerful magic-based attack (instead of being based on physical attack power), the Trickster, which has Nu Mou-like Magic Power, Ninja Speed, and Cards which have extremely high range, as well as access to Halve MP, you can spam Ultima Sword EVERY turn (as long as you also have MP Channeling active), one-shotting pretty much every enemy, before they can even move, from halfway across the stage.
Another good option here is to equip your resident Sage with two Reverie Shields, the Azure Tear, Red Shoes, and Ninja Gear. This puts his evasion up to 70%. Combine this with the aforementioned method of using Ultima every turn and you've got a supposedly spell-oriented class, on a Nu Mou no less, running around the field, dodging the vast majority of attacks, and PUNCHING ENEMIES IN THE FACE FOR MASSIVE DAMAGE since Ultima uses your weapon animation and you don't have a weapon equipped. And this is just the primary job, you can stick White Magick on the secondary and you've got an unkillable Ultima machine. Of course, this isn't remotely feasible until incredibly late in the game because the Azure Tear can't be obtained until the third ascent of Brightmoon Tor, and without it you can only reach 50% evasion. Which is still pretty good.
Spear wielding Bangaas also make good abusers as their Ultima attack will target two squares instead of one.
One of the subtly strongest moves in the game is Smile Toss, a skill of the Moogle Juggler. It does the exact same thing as the Time Magic "Quicken", except it does not cost any mana to use. A hasted Juggler (which has excellent speed growth) using his turns to Smile-Toss his slower but more powerful teammates can completely subvert the usual turn order of the battle, allowing you to control the tempo of battle by having your powerhouses take many more turns than they normally would. Having two Moogles smiletossing each other will let you fill their mana up as much as you want and position them wherever you like on the battlefield, allowing you to even beat certain missions before the enemy even gets a turn. Careful use of this strategy is as disgustingly powerful and possibly moreso than simple CT calculations in classical Final Fantasy Tactics, as you can even reprioritize turn orders and force their opponent's turns to be delayed as a result of a Quickened character stealing their turn opportunity.
Mitigated by his lack of status protection, allowing you to cripple him with your status ailment of choice. The real pain is the high evasion granted by his shields, which makes it dicey to actually hit him.
Ether Shot is almost required to properly abuse many Nu Mou jobs and completely bypasses the MP system. Additionally a Cannoneer can abuse the Half MP/Ultima combo with less power (but the same range) as a Trickster.
An understated one, but the auction houses can get you really good items early on in the game. If one was so inclined, from about a fourth of the way into the game (with sidequests it can feel more like 1/8th) a player could potentially reproduce a majority of the game breakers mentioned on this list by using the cottage in Aldanna Range to sleep past a year, select "exhausted" or the third option after Luso mentions it and the first option after the first rest, to restart the auctions and refresh their rewards, allowing for a great selection of abilities before the Lord of the Flowsand fight.