"Far cry" means very different ("far different" is acceptable English in my region).

The Oxford Learner's Dictionaries website is an excellent resource.

far

https://www.oxfordlearnersdictionaries.com/definition/english/cry_2#far_idmg_23

​a very different experience from something

synonym remote

In addition to Chris and Dan Smith who already provided a good explanation.

Expression: be a far cry from sth

Meaning: to be completely different from sth.

Examples: 

1- This new shopping center is far cry from downtown.

2- His new school is far cry from the previous one.

3- Her final result is far cry from the midterm examination.

So, as per the details provided above, if you see your following sentences, they are producing the same meaning with and without a far cry.

(With a Far Cry) She viewed all of it as being a far cry from the high hopes that her family had for Aaron.

(Without a Far Cry) She sees all of it as being very different from the high hopes that her family had for Aaron.

Chris is correct. I'll add a couple of things.

1) "A far cry from [something]" is quite common in US English; it's a very natural way of adding emphasis and informality to the idea of "very different from."

2) It's a good example of an idiom that native speakers "just know." We pick it up as a unit. I never thought about analyzing it until this instant. It isn't a combination of the meanings of "far" and "cry." It's like a word in itself.

3) Short pocket dictionaries for use by travelers and beginning learners may just have entries for individual words. Bigger dictionaries, like desk dictionaries, and no-cost online dictionaries, will include many colocations and idioms. Do not hesitate to check a dictionary. I like the American Heritage dictionary--online and as a print dictionary--not just because it is a US English dictionary, but also because the quality of its definitions seems very good, and it has good usage notes here and there, too. Anyway, the entry for far,

https://ahdictionary.com/word/search.html?q=far

lists meanings for "far" as adverb and adjective, and then a long list idioms, including:

1. A long way: stuck at the airport in Memphis, a far cry from Maine.

2. Something that is very different from something else: This food is a far cry from what we got in the cafeteria.