Learn English – One word for a “very tough task”

There is monoculus for a one-eyed person but OED says that it is obsolete.

†2. A one-eyed person or creature. Obs.

Etymology from OED:

< post-classical Latin monoculus the caecum (1363 in Chauliac), a one-eyed person or creature (7th cent.; from 12th cent. in British sources), irregularly < ancient Greek μονο- mono- comb. form + classical Latin oculus .

_{The word is perhaps attested earlier in sense A. 2 as a surname, Simon Monoculus (1212), though it is unclear whether this is to be interpreted as Middle English or post-classical Latin.}

For someone who is blind in one eye or wearing an eye-patch, it doesn't seem like there is a specific single word. (For example, there is borgne in French.)

However, there is again an obsolete word for this sense: purblind.

2. †a. Blind in one eye. Obs.

Urbandictionary mentions pirate-eyed as a slang term but it is described as a specific case:

"Pirate-eyed" is a condition resulting from over use of the iPhone or similar device in the dark or dimly-lit environment whilst favoring one eye. The resulting condition causes a temporary focal imbalance akin to having a patch over an eye.

The words you're looking for are:

dereliction (of duty)

From oxford:

The shameful failure to fulfil one’s obligations

As in, "the prosecution team were guilty of dereliction of duty for failing to disclose evidence"

and derelict

From oxford:

chiefly North American Shamefully negligent of one’s duties or obligations

EDIT: Although derelict does have other meanings, as noted in the comments.