Aikiki is a good contender.
Nechisar Nightjar? I'd say a bird that we only know about because we found a dead one once is going to be pretty hard to spot.
On the upside if you do, you could make birding history.
Some random thoughts (and I see Jurek already asked the same question):
Is Nechisar Nightjar even a valid taxon?
I know of a guide arranging a private boat for Narcondam Hornbill April 2026.
Blue-eyed Ground-dove is off the radar for the unforeseen future, as the reserver will be closed for visitors for at least the next 2 years. Official statement from SAVE Brazil is coming soon.
There are several factors that make a bird hard: logistics (to even get to a certain place: altitude, walking or boat distance, safety, accessibility), how much targeted searching contributes to finding the bird (some species are very hard but the more you search, the more chance, other birds don't seem to have such a effort / chance of encounter correlation), rarity and thus overal chance of encountering maybe the last few examples of the bird, skulkiness, weather and distance (some birds are always in places with bad weather and / or only to be seen at large distance),...
Some hard birds I can think off:
Snow Mountain Robin (currently out of bounds, not allowed to go there), Afghan Snowfinch (not very safe to visit Afghanistan), Sulu Hornbill (not very safe, for decades with seemingly short 'safe' windows that only the very brave (or reckless) dare to use), Narcondam Hornbill and many other one-island endemics (mainly boat distance and sometimes accessibility / landing possibilities on the island), Red-billed Ground-cuckoo (far away from everything and still a very skulky bird), Maned Owl, some of the birds in isolated small mountain ranges in Papua, e.g. Foja Mountain birds such as Bronze Parotia, Sillem's Mountain Finch (altitude), some partridges and rails in SE Asia, Congo Peacock, Akikiki (a handful left and not at all easy to get in the right area), Yellow-crested Helmetshrike (refound, but the whole area seems unsafe again),... I can think of 100 more.
But there are so many birds that aren't even on the in-fashion-by-even-the-craziest-world-birders radar. E.g. who in this topic is thinking about targeting Jos Plateau Indigobird, Lufira Masked Weaver, Western Wattled Cuckooshrike or Niam Niam Parrot anytime soon? I know people who have seen the Weaver and Niam Niam Parrot, but those seem to be one-off occasions. Some of these birds (like the Weaver) aren't too difficult, it's about getting there. Maybe that's the same for the Parrot.
The Cuckooshrike is a bit complicated to get there (but doable), it's probably most of all a hard bird to connect onto, and I don't see anyone in the world birding scene mention this (imho stunning) bird once, while they do mention all the 'popular' goodies (I admit I do the same!). So I don't even know anyone who has tried to see the Cuckooshrike or will try to do so in the near future. That Indigobird... Who wants to go to central Nigeria or N-Cameroon these days? Maybe it isn't even hard to get there or to find the bird, but who besides the locals is seeing those birds?