Expresses the idea that 'despite something, action was carried out', simply translating to 'without being phased by something'.
Long explanation:
The 'Nounをものともせずに' grammar point means that something which could potentially be a hindrance or challenge was not taken into account or cared for, in carrying out an action. The literal translation could be ‘not making something an object’, hence meaning actions were performed without any phasing or distractions by it.