IPA: /ˌɪrɪˈproʊtʃəblɪ/
KK: /ɪrɪˈproʊtʃəblɪ/
In a way that cannot be criticized or blamed; perfectly.
She performed her duties irreproachably, earning the respect of her colleagues.
Irreproachably → It is formed from "ir-" (meaning not), "reproach" (from Latin "reprochare", meaning to blame or criticize), and "-ably" (meaning in a manner). The word means in a manner that cannot be blamed or criticized.
Think of 'not' ('ir-') allowing for 'blame' ('reproach') — that's why irreproachably means acting in a way that cannot be criticized.