Below is a list of difficult fish to quarantine, with specific recommendations on QT strategies for each group of fish.
Angelfish (and their sensitivity to copper)
I've never figured out if angels being sensitive to copper is a "thing" or not. They do seem to fare a little better in Cupramine vs. chelated copper (e.g. Copper Power).
QT strategy: Best to just dose Chloroquine (better tolerated) in lieu of copper. If copper must be used, raise it gradually (over 2-3 days.) If your angelfish stops eating after raising the copper level, do a water change to lower it until the fish resumes eating. Most angels will show symptoms of appetite suppression, lethargy, heavy breathing before just dying in copper.
Prone to uronema, internal flagellates, and deep water anthias can develop swim bladder disorders due to improper collection/decompression. To complicate matters, anthias can be sensitive to medications (never use Chloroquine on them) and the deep water species are sometimes difficult to get eating. You also have to watch out for aggression between them. Many hobbyists try to QT a shoal consisting of a dominant male and/or harem of females. Two males are a no-go, and the male will assert his dominance over all the females. While females too maintain a pecking order among themselves. So, you have to watch closely to ensure none of your anthias are being bullied to death. (If you ever see two locking mouths, one needs to be removed ASAP.) This article explains anthias behavior in much greater detail: https://www.liveaquaria.com/PIC/article.cfm?aid=266
For reasons outlined above, anthias might be the hardest fish there are to QT!
QT strategy: Dose Metronidazole ASAP, but raise copper very slowly (4-5 days) when treating anthias. If they are eating, soak their food with metronidazole for 10-14 days. Seachem Focus can be used to bind the medication to the food. If your anthias stops eating after raising the copper level, do a water change to lower it until the fish resumes eating. Most anthias species have a high metabolism and need to be fed at least 3 times per day.
Due to their sensitivity to meds, anthias are also perfect candidates for Black Molly QT: Black Molly Quarantine
Blue Spot Jawfish
Prone to their very own named disease: Blue Spot Jawfish Disease. It is uncertain whether this disease is parasitic or bacterial in nature.
QT strategy: Treat with Metronidazole (e.g. Seachem Metroplex) + Kanamycin (e.g. Seachem Kanaplex) for 10-14 days. This combination addresses both parasites + harmful bacteria.
Very prone to "red sores" i.e. uronema, both externally and internally. This is one disease you never want to get in your DT because going fallow will not eliminate it.
QT strategy: Treat with Chloroquine or Metronidazole IMMEDIATELY upon receiving. Because uronema can spread internally, it is also important to soak their food with metronidazole for 10-14 days. Seachem Focus can be used to bind the medication to the food.
Not difficult to QT, but sometimes Brooklynella (which they are very susceptible to) is not prophylactically addressed.
QT strategy: Always chemoprophylactically treat for brook when quarantining clownfish using one of the following options:
Dose metronidazole every 48 hours for 10-14 days.
Dose Chloroquine phosphate (15 mg/L or 60 mg/gal) once.
90 minute bath using Ruby Reef Rally before the fish enters QT.
45 minute bath using formalin before the fish enters QT.
Copperband Butterflyfish (and other finicky carnivores)
The biggest challenge with these is getting them to eat. Copperbands are relatively tolerant of copper & other meds, but somewhat prone to uronema and bacterial infections. Both diseases will present as red looking sores on the fish's body.
QT strategy: If your new Copperband is pacing or swimming frantically, odds are he will have no interest in food. Once he settles in, try the easiest foods to acquire first: Frozen brine, mysis, PE mysis, etc. (Sometimes you get lucky.) There is also a self-adhesive paste called "Masstick" they will sometimes eat. Next up would be to try live blackworms or white worms. And finally, a frozen clam or oyster on the half shell. (Don't leave either in the QT for too long.)
Due to their susceptibility to infection, butterflyfish benefit from a 45-60 minute bath using Nitrofuracin Green upon arrival. Once in QT I recommend copper + Metronidazole, or Chloroquine phosphate to treat ich, velvet, brook, uronema.
Gobies ** Prolific tank jumper, so use a secure lid **
The biggest challenge to quarantining these is preventing them from jumping out. They also sometimes carry intestinal worms + internal flagellates.
QT strategy: Use a tight fitting lid over the QT, ensuring even small openings are made secure. (Gobies can wiggle through tight spaces.) Once they are eating, soak their food with API General Cure for 10-14 days. This will eliminate any internal issues. Seachem Focus can be used to bind the medication to the food.
Disease-resistant fish which handles most meds just fine (EXCEPT COPPER). The biggest challenge to quarantining one of these is feeding due to its need for pods.
QT strategy: If you can get a captive bred specimen (e.g. ORA, Biota) already eating frozen or pellets, that is a huge help. Otherwise you're in for a rough go of it. Some have luck offering baby brine shrimp, Masstick, live blackworms, fish eggs... If you ever see "Nutramar Ova" (now discontinued), grab some of that! You can dose pods (or add LR/chaeto with pods), but that only works in a non-medicated environment.
When quarantining a mandarin, you want to get the specimen into your DT (where the pods are) as quickly as possible. The fastest way to do this is to treat with Chloroquine phosphate (see CP Protocol #1) and then transfer the fish directly into your DT after 10-14 days. This strategy is not without risk, so transferring to an observation tank (with LR/chaeto/pods) would be a safer option. You would then black molly test the observation tank to ensure the mandarin is "clean": Black Molly Quarantine
This is actually an easy fish to QT if you can just get it eating. They are tolerant of most medications and not overly susceptible to many diseases.
QT strategy: Similar to a Copperband, try offering brine, mysis, blackworms, clam, oyster, etc. However, unlike most butterflies a Moorish Idol is omnivorous so you can also try feeding nori in QT. (Soak nori in RODI water if medication(s) are being used, so it absorbs the taste of that and not the medication.) Keep in mind that Moorish Idols have very high metabolisms and thus require multiple daily feedings.
Puffers, Lionfish, Eels and other copper intolerant species
Relatively easy to quarantine, but these fish do not always tolerate copper well.
QT strategy: Puffers will sometimes do OK in chelated copper (e.g. Copper Power). However, puffers, lions and other copper intolerant species do best if treated with Chloroquine phosphate. Hyposalinity (aka Osmotic Shock Therapy) is another option for puffers, but it only treats Ich + Flukes.
Intolerant of copper and (probably) Chloroquine as well. Seahorses are prone to gas bubble disease and certain bacterial infections.
QT strategy: Seahorses do best at temperatures of 70-74F, which discourages harmful bacteria from propagating. They are susceptible to infections which can afflict their snout, tail and gut. Triple Sulfa & Furan-2 are two recommended antibiotics to use. Diamox is the best medication to keep on hand for treating gas bubble disease, and an insulin syringe with a 26-gauge needle can be used to release excess gas from a male's pouch. I've seen Bio-Bandage (Neonmycin-based topical gel) recommended for lacerations.
Pipefish are relatively hardy, but like seahorses do best in a low flow environment. Both seahorses & pipefish are ideal candidates for: Black Molly Quarantine
Sharks, stingrays and eels
Scaleless fish which are intolerant of copper.
QT strategy: Chloroquine phosphate is the treatment of choice for eliminating ectoparasites found on these fish. Dimilin or Dylox can be used to deworm / remove parasites with an exoskeleton found on sharks & rays.
Tangs (primarily Acanthurus spp.)
We've all heard about how "hard" Achilles & Powder Blue Tangs are to keep. They're not. However, they do require a parasite free environment (due to their thin slime coat) and strong water flow for increased oxygen (they are typically collected in crest zones).
QT strategy: Point a powerhead (or run an air stone on high) towards the surface of the water in order to create a disturbance/ripple effect. This will increase gas exchange and infuse more dissolved oxygen into the water. It's also a good idea to prophylactically treat with copper or Chloroquine, in order to eradicate any ich/velvet they may be carrying.
Wrasses (Fairy, Flasher & Leopards) ** Prolific tank jumper, so use a secure lid **
There's a reason they are sometimes referred to as "pain in my wrasse". These fish flat out don't like being in quarantine; especially a rockless, bare bottom environment. They are prone to flukes and internal parasites/intestinal worms. Wrasses are not a big fan of most medications (so take care never to overdose with them.)
QT strategy: Since these fish prefer to lay on sand sometimes (Leopards will burrow), it is advisable to have an area of sand in the QT for them. (Sand in a glass Pyrex bowl works.) You definitely want to deworm all wrasses using praziquantel. Fairy wrasses, Leopards, Halichoeres spp, Anampses spp, Labroides spp, Thalassoma spp, Pseudocheilinops spp tolerate Chloroquine well; Flashers, Coris spp & Pseudocheilinus spp DO NOT. When using copper, most wrasses seem to do better in chelated copper (e.g. Copper Power) than ionic (e.g. Cupramine). Regardless of brand, raise copper very slowly (4-5 days) when treating wrasses.
To deal with the internal problems (you'll see white stringy poo if internal parasites/worms are present), soak food with API General Cure or Fenbendazole for 10-14 days. Seachem Focus can be used to bind the medication to the food.
Being a "pain in the wrasse" qualifies you for: Black Molly Quarantine