Because of having been accused of polluting huge areas of the

Correct Option : C

Original sentence:
Because of having been accused of polluting huge areas of the Ecuadorian Amazon from its oil operations there in the 1970s and the 1980s,
Chevron is currently involved in the biggest environmental lawsuit the world has ever seen.

Elimination steps
1. Because of vs Due to
Due to is an adjective - which indicates it can only modify pronouns and nouns.
Because of is an adverb, which implies it can modify verbs, adjectives and clauses, but not nouns and pronouns.
This both are not required, for the intended meaning of the sentence.
- Additional in option A, in the end the time frame "the 1970s and the 1980s" it shows as they are same era, the correct form must be,"the 1970s and 1980s"
Eliminate : A, and (E + with usage of "being" is wrong).

2. because of SV agreement error, wrong usage of "their" oil operation, the correct pronoun is "It's" refer to Chevron, which is in non underlined sentence
Eliminate D, and (B because of openning with having been, which is not required)

3. In sentence B
- Having been behaves as a "Subject" of the sentence, which makes it grammatical incorrect, it is past participle form and used to emphasize that a first action has been completed before the second option begins, addition to this, it is used to modify Noun,if used at beginning of the sentence, and mostly in between sentence to modify adverb.
This usgaes portrait, the intended meaning of sentence wrong.
Eliminate - B

With C
- "accused of" subject modify "Chevron"
- SV agreement, "it's" refer to "Chevron"
- time frame "the 1970s and 1980s" is correct

Makes C correct option