Step 1: Understand the given word.
UNDETERRED means not discouraged or stopped by difficulties; it describes someone who continues fearlessly despite obstacles or threats.
Step 2: Eliminate synonyms.
"Bold" and "gallant" convey fearlessness and courage, making them synonyms of undeterred. "Daunted" (intimidated) is close but less precisely opposite in feeling.
Step 3: Select the best antonym.
"Apprehensive" means anxious and fearful about what may happen, which is the opposite of being undeterred and resolute in the face of difficulty.
\[ \boxed{\text{apprehensive}} \]