They continuously claim that the destruction of the environment is totally all human beings' responsibility.

continuously 是形容词 continuous（连续的）加上副词后缀 -ly 构成的副词形式。continuous 来自动词 continue（继续），表示"不间断地、持续地"。 在这里 continuously 修饰动词 claim，强调"持续不断地声称"这个动作的持续性。