If something must be done or avoided at all costs, it must be done or avoided whatever happens.

Security during the president's visit must be maintained at all costs. 要不惜一切代价确保总统在访问期间的安全。

He wanted her at any cost, even if it meant giving up everything he had. 他不惜一切代价要得到她，即使这意味着放弃他自己所拥有的一切。