Official Explanation
Split #1: the word "hitters" is followed by a modifying clause ---- what word should begin this clause? In informal language, one could say "hitters that …", but technically we need "hitters who …", because we use "who" for people and "that/which" for objects. The GMAT upholds this distinction in its own writing, although it rarely tests a "who" vs. "that" split in the context, so this aspect of this question focuses on a subtlety rarely tested on the GMAT. Only (C) & (D) use "hitters who …", so only these two are correct.
Split #2: "corresponding" vs. "correspondingly". The GMAT loves adverb vs. adjective splits, especially with a tricky adjective such as "corresponding." Adjectives modify nouns and adverbs modify verbs or adjectives. Here, the adjective "corresponding" would have to modify the noun "on-base percentages" ---- these OBPs correspond to what? What the sentence is trying to say is: when the batting average is high, the OBP is also high --- the thing that "corresponds" is the fact that when one is high, the other is high. Therefore, we need the adverb "correspondingly" modifying the adjective "high", to emphasize that the "highness" of one corresponds to the "highness" of the other. Only (A) & (C) have the correct choice "correspondingly high."
Split #3: three choices, (B) & (C) & (E) have the sleek elegant phrase "the highest career batting average" --- clear and direct. Choice (A) has the wordy phrase "career batting averages that are the highest" and choice (D) similarly has "career batting averages which are the highest." Arguably, either "that" or "which" could be grammatically correct in this context, but the point is: both of these, even if grammatically correct, are far too wordy and indirect. Such overblown indirect phrasing will never be correct on the GMAT SC.
For all of these reasons, the best answer is (C).