The phrase means undertaking a task despite all seemingly insurmountable opposition or probability. Often the chances of success are very low. Against all odds.

表示要冲破一切险阻去做某事，尽管这件事情看起来很有可能会失败。

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The case is so strong that, despite vast public opposition to Medicare cuts, policymakers of all stripes in Washington favor them.

FORBES: On Medicare, the American Public Is Dangerously Out of Touch with Reality

Despite losing three more clashes against top American opposition, Farr went the distance with all of them.

BBC: Tommy Farr: Boxer who fought his way out of pits