CliffNotes for the I~III Delve NMs:
Volatile Matamata - This is the easiest I~III NM for Morimar, and can be done with as little as 3 people. Has incredibly high HP (around 2.2 million), but damage from different sources increases and decreases on a sliding scale. The NM will do a TP move at set intervals, between 45 and 60 seconds from the last one, and when it begins charging the TP move it will shift the damage scale to either reduce magic damage taken and increase physical damage taken, or increase physical damage taken and reduce magic damage taken. This caps out at seven phase changes and will result in physical weaponskills dealing capped (99,999) damage and normal melee strikes dealing from 15,000 to 80,000 damage depending on job and buffs. The two best ways to go about this would be either using a MNK+BRD+WHM setup and having the MNK punch it until they do 0-1 damage with each punch, at which point they should use Impetus, Focus, and Aggressor to start building Impetus bonus for the next TP move; when it TPs again, pop Berserk and Formless Strikes: your BRD should be giving you maxed/Marcato march (+ madrigals if your ACC is still poor after adjusting gear, food, and other buffs and your BRD has a Daurdabla) and your WHM should be giving you haste; if your gear is properly tuned (max haste + lots of accuracy), you'll be able to kill it before the next TP move without the use of Hundred Fists, but if your gear or buffs tend to be lacking, you'll need to pop Hundred Fists to kill it in time. Alternatively, you can do it with a couple of strong melee DDs, a BRD, a SCH or BLM, and a WHM; have one of the melees hold the NM (do not engage, stand there and provoke/perform other hate-bearing actions and keep PDT set on) while your SCH or BLM nukes it for the first 6 TP moves. Magic damage will deteriorate, eventually reaching 0 on the 7th TP move, at which point melee should go in and kill it. A SCH/RDM swapping into no nuking gear can easily gauge the TP move that the matamata is on without counting TP moves simply by the damage that their nukes are doing; from TP move 1 through 4, tier II spells should be doing damage, however on tp move 5 your tier IIs will start doing 0 damage; switch to tier IIIs for TP move 5, then switch to tier V for TP move 6. You only have to land one nuke for 1 or more damage per TP move as long as the NM is not hit with any physical actions (things like Shield/Weapon Bash count, don't use those).
Perdurable Raptor - This one can be done with as little as 6-8 people. You'll need a couple of strong DDs with proper gear sets and a bunch of accuracy buffs in order to kill it in a reasonable amount of time (p1 DD DD DD COR BRD WHM, p2 SCH GEO would work well). The biggest thing for this fight is to deal
zero magic damage, any magic damage done to the NM will cause it to enter a frenzy, increasing its multiattack rate and attack speed dramatically which will usually result in one or more DDs getting killed. Anything that deals magic damage is to be avoided: quick draw, enspells, magical weaponskills, spikes(reprisal), and skillchains. Otherwise it's a normal zerg, try to stun its unique TP move "Whirling Inferno" as it puts a potent attack and defense down debuff on whoever it hits along with a zombie effect (prevents whoever's afflicted from being cured).
Shimmering Tarichuk - This one can also be done with as little as 6-8 people. Use the same setup as for Perdurable Raptor, except try to incorporate a well geared RDM. It gains a powerful poison aura under 50% HP that deals 100HP/tic in damage and can never be removed. Regen V and Embrava help a lot to mitigate this, and Embrava also counters its other major annoyance: Geist Wall spam. It will constantly dispel everyone's buffs, usually leaving you without marches, haste, or whatever as your mages and support scramble to reapply; having a non-dispellable source of Haste and Regen helps a lot for that. You can also put up dummy buffs like intimidation circles, barspells, and auspice in order to reduce the chances of important buffs getting dispelled. The reason you want a RDM is mostly for Silence; it lands on this thing and will be a major asset to you over time as its nukes begin to go off faster and faster as the fight goes on and will deal considerable damage.
Faded Craklaw - Seems to take enhanced damage during TP moves and gains resistance to damage and magical effects after it uses Impenetrable Carapace. Murasamemaru SAMs are very helpful here if you have some, they'll deal considerable amounts of damage to this. Stunning Impenetrable Carapace will also help a lot as it cannot be dispelled and stacks on top of itself.
Aberrant Uragnite - This one takes next to 0 damage when it is popped and will take increasing amounts of damage as you put debuffs onto it, so stack as many as possible. Every time it goes into its shell it will put up a Doom aura, so be sure that all melee run away from it when it goes inside of its shell to avoid dying. Otherwise it's just a normal zerg.
Divagating Jagil - This one is mostly a DPS race. It will cycle through the elements which will cause it to absorb and resist certain elements of magic and cast different spells. It will also have an enspell matching its current element, it starts off doing fairly low damage (80~110), but as the fight goes on it will become progressively more powerful, reaching in excess of 3,000 damage per additional effect. The only ways to counter this are to either kill it before it reaches that point or have your melees ride utsusemi/seiganeye. Having someone capable of stunning Kaustra, Embrava, and Meteor also helps. (Kaustra and Meteor are used during dark phase, Embrava during light)
Unfettered Twitherym - This is mostly a zerg fight, however there are a few caveats. First and foremost, unless your WHMs have Yagrush then bring plenty of remedies, it will spam Blackout giving everyone around it Blind and Paralyze for most of the fight. Under 50% it gains access to its unique TP move, Smouldering Swarm, which deals severe AoE damage and leaves a powerful Burn effect: trying to stun this would be beneficial. It also gains near immunity to all forms of damage at 49% and 24% HP, the only way to remove it is by performing a skillchain that correlates with the current day of the week. Light and Darkness work for this, so just use one of those based on which day it is.
Supernal Chapuli - It's best to use a bunch of MNKs on this guy. The idea here is to not weaponskill him or use job abilities like shield bash or weapon bash, each weaponskill and damage dealing job ability will increase his evasion, and by the 11th weaponskill he will have a capped evade rate. He has two modes for his TP move which he switches between by using Nature's Meditation: mode one is comprised of normal chapuli TP moves (Tegmina Buffet, Sanguinary Slash, Sensilla Blades) while mode two introduces his unique TP move: Orthopterror. He will use
only Orthopterror during this mode, and it absolutely sucks; it deals a high amount of damage and terrorizes anyone in front of him for a moderately long amount of time along with a strong knockback effect. I suggest keeping your DT sets ready during mode 2 to mitigate the impact.
Transcendent Scorpion - This one's mostly a normal zerg except for one thing: Earthbreaker. Prepare to jump out of a window, because this is the most annoying thing ever. On top of dealing severe physical damage, Earthbreaker will stun everyone who is hit by it for several seconds. Did I mention that it has a range that exceeds maximum casting range? You can force it to deal 0 damage by keeping at least one debuff up on the NM at all times, but be sure to pay attention as every time the message "The spring returns to your step!" appears in the chatlog, it means he's wiped all of his debuffs off and that they need to be reapplied. Unfortunately, while you remove the severe damage part of it, it will continue to stun absolutely everyone. Over and over. I suggest having as many people as you can sub NIN in order to avoid getting stunlocked.