What (does agonize me most) is not this criticism, but the trivial reason behind it.
The bracketed part of the sentence can be replaced be-

The correct replacement for the bracketed part "does agonize me most" is "agonizes me most." The revised sentence would be:

"What agonizes me most is not this criticism, but the trivial reason behind it."

Explanation:

1. "agonizes me most": This phrase is grammatically correct and maintains the proper structure of the sentence. The verb "agonizes" is used in the present tense, and "me most" is the appropriate order for expressing intensity or degree.

The other options:

2. "most agonizing me": This option has an incorrect word order. The adjective "agonizing" should come before the pronoun "me" to form the correct structure.

3. "agonizing me most": While the words are correct, the order is not. The proper order is "agonizes me most" for expressing intensity or degree.

4. "I most agonized": This option changes the verb form to the past tense ("agonized") and alters the meaning of the sentence. The original sentence discusses a present concern, so changing to the past tense would be inappropriate.