1
general::
Also, at any cost or price. Regardless of the expense or effort involved, by any means. For example, Ann told the doctor to preserve her mother's sight at all costs, or It seems the company plans to develop the product at any cost, or I'm determined to get vacation time at any price. [Mid-1800s]
American Heritage Idioms
2
general::
Phrase(s): at all costs [and] at any cost
Fig. regardless of the difficulty or cost; no matter what. • I intend to have that car at all costs. • Mary was going to get that job at any cost.
McGrawhill's American Idioms And Phrasal Verbs