Know thy enemy
Let us first look at our foe, the Heraldic Imp
Level 78-81
Black Mage
Approx. 2000-2500 HP
Abilities:
Abrasive Tantara - Induces amnesia, which prevents the use of job abilities or weapon skills.
Deafening Tantara - Causes silence. You'll want to remove this ASAP for obvious reasons.
Since they are BLMs, let's look at the heat they're packing.
Fire III - Cast time: 6sec.
Blizzard III - Cast time: 6.25sec.
Thunder III - Cast time: 6.75seconds.
Firaga II - Cast time: 5.25sec.
Thundaga II - Cast time: 6sec.
Sleepga - Cast time: 3sec.
Sleepga II - Cast time: 3.5sec.
Poisonga II - Cast time: 1.5~2sec., enemy only, strips shadows like every other Aoe spell
It has access to a number of other spells, but for the most part these are the ones to be wary of.
You can find these in the area near the Azouph Isle staging point, or Hedive Isle, accessed through Alzadaal Undersea Ruins (Nyzul Isle staging point). However, expect to compete with exp parties with the former, and the threat of soulflayers in the latter area. If you choose Azouph as your battleground, try not to fight near the swamp, especially at night or if it's raining. If you get into low HP during an imp fight, you might have some company in the form of a jnun. At this point you're toast.
Know thyself
Here's what you will need to be able to solo these beasties.
-Be at least BLU74. You can probably get away with it before 74, but it's exponentially safer with utsu:ni.
-A leveled NIN subjob with Utsusemi: Ni (if you're at this point you should have these already
-Echo drops and shihei by the truckload (if you get silenced and can't finish the imp off in time, you're a dead duck).
-The "big three" multi-hit damage spells (Frenetic Rip, Hysteric Barrage, Disseverment). You could probably stick something else in place of disseverment, but you won't get the same punch.
-The auto-refresh trait. You can get this for 9 points with Actinic Burst/Plasma Charge or Self-distruct/frightful roar/plasma charge. For those without sea, self-distruct/cold wave/frightful roar/voracious trunk.
-Head butt (this is of pivotal importance)
-Refueling for haste
-Magic fruit for those moments when utsusemi is down and you're getting smacked around, or worse yet if you eat one of those 500+ -aga spells as a result of your head butt failing to connect.
-Diamondhide or metallic body to soak up any DOT effects that would prevent you from resting MP after the fight.
Frenetic Rip recast is 28 seconds (25 with refueling).
Hysteric Barrage recast is 28 seconds.
Disseverment recast is 32 seconds (28 w/ haste).
Now let's look at the fight itself.
Find your imp, buff up with refueling, utsusemi, etc.
Open the fight with a head butt since the imp usually opens the fight by casting a spell.
CA+Disseverment. Why do this now with no TP? One word - amnesia. Also, with CA active, you'll hit harder since its secondary stat modifier, DEX will come into play.
Alternate between head butts and damage spells and restoring shadows until dead.
You can often down the imp 5-7 spells, depending on their damage output. If I find an imp is low on HP after a damage spell, I'll follow up with another one in lieu of a head butt if I'm confident I can down it after said spell and/or a couple of sword swings.
Head butt not only buys you valuable time, but can also avert the threat of any nasty spells.
Things can and do go wrong at some point, even with the best setup and capped blue magic merits. The imp may get off a poisonga or sleepga and strip your Ni shadows and/or your head butts may get resisted (one time I had an imp resist four head butts in a row). DO NOT PANIC! Fire off another head butt and magic fruit yourself and get back in there. You may have bought yourself a few more seconds to the point where another Ni might be up, so you can fire off another head butt and throw your shadows back up. It can be difficult to recover from such situations.
The poison effect from disseverment can also be a lifesaver. It does a nice 12hp/tick on your foe, just as if an aern had done it on you. I've had instances where my HP was in the double digits (hell even single digits) and I had just enough MP for a single head butt and I couldn't get shadows back, and seconds later "The Heraldic Imp falls to the ground."