Ctenomorpha gargantua aka the Lady Gaga-ntuan or gargantuan stick insect is one of mine. Lives high in the canopies and a female found in North Queensland was only 50 cm long.
Closer to home is the goblin spider Ischnothyreus darwini. Tiny wee spider found in monsoonal forests including places less than one kilometre from one of my work locations.
I’d love to be the first to post an obs of the colossal squid Mesonychoteuthis hamiltoni, preferably alive in it’s natural habitat. Never going to happen 
Algidia homerica is something I would look for if I am ever in the Homer area. It is only known from a single female collected in the 40s. So would be interesting to add to knowledge of it.
Not a particular species, but there is a phylum of animals called Loricifera. They are meiofaunal marine organisms (meaning, 0.1-1 mm in size) and can only be found in interstitial habitats (between sand/gravel). They attach themselves to grains of sand or small rocks so it’s close to impossible to get one of them isolated from the sediment.
The small size as well as the habitat not being sampled a lot mean that these animals are very rarely documented in general, and there are currently 0 observations of the phylum on iNat.
Image: Wikipedia
The dozens of springtails here in Ohio that no one has observed. Really isn’t that hard to find them, the hard part is actually keying them to species!
The spider genus Arkys is my favourite. I still have a few described species to find and there are at least two or three that don’t appear to have any observations as yet on iNaturalist. Obviously I’d love to find those
not on inat for the state of Wisconsin, I have been looking for Tropidoclonion lineatum (lined snake) in WI for idk how much time, probably hundreds of hours looking and im being convinced they aren’t even real
Spiraculum beddomei whose type locality is some hill in my city (its recently rediscovered - https://www.researchgate.net/publication/355028581_Rediscovery_of_an_endemic_snail_Spiraculum_beddomei_Blanford_1866_Mollusca_Cyclophoridae_with_notes_on_its_zoogeography_and_natural_history from another location few hundred kms away)
I just cant figure out where the historical Kimerty/Kimery/Kimety hill of its type locality is now (nothing on google or https://www.peakfinder.com) or if its typo/old colloquial name or whether that hill already vanished from human development (which isnt uncommon here) 
i already found few other endemic macro snails for my region.
