The Cyclops is a very dangerous quest nemesis. Fighting him one-on-one is not advised, as he is faster than a normal giant and gets two strong weapon attacks with the Staff, which is guaranteed to drain a level each time it hits you.
As with other quest nemeses in 3.6.1, the Cyclops respects the scroll of scare monster. If you can engage him on the stairs with one on the floor, you can easily beat him to death.
Fortunately, the Cyclops is susceptible to most magical attacks due to his MR of 0. Sleep is guaranteed to work on him, although the ray may miss due to his AC of 0. A wielded potion of sleeping is more likely to hit, and a wielded potion of polymorph is highly likely to cripple him, along with the wand of polymorph, which will never miss. Of course, a wand of death is also very safe here.
And after he had milked his cattle swiftly,
he again took hold of two of my men
and had them as his supper.
Then I went, with a tub of red wine,
to stand before the Cyclops, saying:
"A drop of wine after all this human meat,
so you can taste the delicious wine
that is stored in our ship, Cyclops."
He took the tub and emptied it.
He appreciated the priceless wine that much
that he promptly asked me for a second tub.
"Give it", he said, "and give me your name as well".
Thrice I filled the tub,
and after the wine had clouded his mind,
I said to him, in a tone as sweet as honey:
"You have asked my name, Cyclops? Well,
my name is very well known. I'll give it to you,
if you give me the gift you promised me as a guest.
My name is Nobody. All call me thus:
my father and my mother and my friends."
Ruthlessly he answered to this:
"Nobody, I will eat you last of all;
your host of friends will completely precede you.
That will be my present to you, my friend."
And after these words he fell down backwards,
restrained by the all-restrainer Hupnos.
His monstrous neck slid into the dust;
the red wine squirted from his throat;
the drunk vomited lumps of human flesh.