Two thoughts about this verse.
One, when it says "greatly shaken," I feel like the writer is acknowledging that troubling times and hardship can shake you. They can produce some fear and anxiety, and the writer isn't ignoring that reality.
Two, "I shall not be greatly shaken" is actually only two words in the original Hebrew: rav mowt (רַב מוֹט). Rav means much, many, greater than. Mowt means to totter, shake, or slip. I'm no translation expert, and I can see how the actual translators would translate the way they do. I also wonder if it could be translated like "he is stronger or greater than great shaking."