Step 1: Apply the preposition rule for "despite": "despite" already functions as a preposition on its own and is never followed by "of"; only its synonym phrase "in spite of" takes "of". So "despite of" is always incorrect English.
Step 2: Test each option against this rule. Option (a), "Despite of his best effort", keeps the faulty "despite of" and additionally changes "efforts" to the singular "effort", which is a needless, unrequested change. Rejected. Option (c), "In spite his best efforts", drops the required "of" from "in spite of", creating a new error rather than fixing the original one. Rejected.
Step 3: Option (d), "No improvement", would only be correct if the original had no error, but "Despite of" is a textbook double-preposition error, so this is rejected.
Step 4: Option (b), "Despite his best efforts", removes the incorrect "of" and keeps "despite" as a stand-alone preposition directly before the noun phrase, which is the standard correct form.
Correct option: (2) Despite his best efforts.