IPA: /ɪnˈtræn.sɪ.dʒənt.li/
KK: /ɪnˈtræn.sɪ.dʒənt.li/
In a way that shows refusal to change one's views or to agree about something.
She intransigently refused to compromise on her principles during the negotiation.
Intransigently → It is formed from "in-" (meaning not) and "transigere" (meaning to come to an agreement or compromise). The word describes a manner of being unwilling to compromise or change one's position.
Think of someone who is 'not' ('in-') willing to 'come to an agreement' ('transigere') — that's why intransigently means refusing to compromise.