Choose the option that best completes the sentence using an appropriate…

Concept: In a sentence-completion blank every offered word is already an adjective, so grammar cannot decide the answer; the logic of the sentence does. "Despite" is a concessive preposition: it introduces a circumstance that would normally stop or discourage the action stated in the main clause. The adjective it governs must therefore name an obstacle, and the kind of obstacle is fixed by whatever the main clause says was overcome.

Application: The main clause here says the rescue team "continued their operation without hesitation". Hesitation is the reaction that risk to one's own safety normally produces, so the circumstance being conceded has to be a dangerous one. "Hazardous" means involving risk or the possibility of harm, and "hazardous conditions" is the standard collocation for surroundings that threaten safety, which is exactly the obstacle that "Despite" sets up.

Cross-check: Each offered adjective is tested against two requirements: it must describe the surroundings, and those surroundings must be something a rescue team would have to overcome.

Completed sentence: Despite the hazardous conditions, the rescue team continued their operation without hesitation.