～をものともせずに without it becoming, being a problem: without being beaten

「～に負けないで」
Refuse to give in to difficulty;s tand bravely against the odds. Note - not used for speaker's situation.

（１）山田選手はひざのけがをものともせずに決勝戦に出ました。
Without worrying about the injury to his knee, Yamada appeared in the final.

（２）救援隊は山崩れの危険をものともせずに、生き埋めになった人達の捜索を続けた。
Indifferent to the danger from the landslide, the search for people buried alive continued.