Explanation:

The original sentence is erroneous.

Reason: The correct idiomatic expression in this sentence is ‘broken the back of ' and not ' breaking the backbone of’.

Break the back of (Idiom):

Meaning: Accomplish the main or hardest part of a task.

E.g.: We've broken the back of the problem.

 Hence, ‘broken the back of’ should be used in place of ‘breaking the backbone of’ to make the sentence grammatically correct.

Among the given choices, only option C replaces the given bold part most appropriately.

The sentence after replacement becomes:

India has already broken the back of GST implementation but there is still a long way to go.

Option C is hence the correct answer.