lord of the rings - Who were the greatest archers in Middle-earth?

Human

According to Tolkien, the greatest human bowman was Duilin, son of Duinhir; the leader of the Men from the uplands of Morthond who fought in the battle of Minas Tirath.

In his "Unfinished Tales", Tolkien specifically refers to him as being a soldier of impeccable physical prowess and has this to say about his abilities with a bow;

Now the folk of the Swallow bore a fan of feathers on their helms, and
they were arrayed in white and dark blue and in purple and black and
showed an arrowhead on their shields. Their lord was Duilin, swiftest
of all men to run and leap and surest of archers at a mark.

---

Orc

The orcs are invariably described as a bit crap with a bow, relying on mere force of numbers and volume of (poisoned) arrows to do damage:

Behind them orc-archers crowded, sending a hail of darts against the
bowmen on the walls. - _{^{LotR: TTT}}

and

Dismayed the rammers let fall the trees and turned to fight; but the
wall of their shields was broken as by a lightning-stroke, and they
were swept away, hewn down, or cast over the Rock into the stony
stream below. The orc-archers shot wildly and then fled. _{^{LotR: TTT}}

and

But orc-arrows are plenty, and the sight of one would not be taken as
a sign of Doom by Boromir of Gondor. _{^{LotR: TTT}}

and

The orcs hindered by the mires that lay before the hills halted and
poured their arrows into the defending ranks. - _{^{LotR: RotK}}

Elves

Arguable. Certainly Beleg (A.K.A. "Beleg the Archer", A.K.A. "Beleg Longbow") is repeatedly called out as being an exceptional archer and possessing the ability to fire arrows great distances:

Moreover Beleg the Archer was great among the people of Doriath; he
was strong, and enduring, and far-sighted in mind as well as eye, and
at need he was valiant in battle, relying not only upon the swift
arrows of his long bow, but also upon his great sword Anglachel. And
ever the more did hatred grow in the heart of Mîm, who hated all
Elves, as has been told, and who looked with a jealous eye on the love
that Túrin bore to Beleg. _{^{The Children of Huron}}

and

Beleg: Elf of Doriath, a great archer; friend and companion of Túrin.
Called Cúthalion ‘Strongbow’.

That said, there's no specific reason to assume he was the single greatest elf archer.