The correct option is A Whoever told you that you're not beautiful- subject
A noun clause is a dependent clause that functions as a noun. It usually
begins with what, whatever, whom, that, why, which, whether and so on. A noun clause can act as a subject, object, predicate
nominative or object of a preposition, in a sentence.
"Whoever told you that you're not beautiful" is a noun clause that functions as the subject of the verb
"has lost" in the given sentence.
('Whoever' is a pronoun that also functions as the subject in the noun clause, 'told' is a verb. Hence the option is a noun clause.)
Hence option A is correct.
Option B is incorrect because 'that you're not beautiful' is a noun clause inside the main noun clause "whoever told you..." whereas the noun clause of the entire sentence is in question.
Option C is incorrect because "has lost his eyesight" is the predicate, it isn't a noun clause; noun clauses do not function as predicates.
(A sentence is made up of a subject and predicate. The subject is a noun or its equivalent that performs an action mentioned by a verb, the predicate contains the verb and every other part of the sentence, except for the subject.)
Option D is incorrect because it is a fragment of the noun clause.