Yes. Resolutely is an adverb (in a firm or resolute manner).
Resolutely means to show determination and purpose. Sentence: She resolutely marched into her boss's office to demand why she was the only one who was underpaid for her job.
Pertinaciously means holding tenatiously; resolutely. She held pertinaciously to her beliefs.
She spoke resolutely, refusing to back down from her position.
I believe the word you are referring to is "intrepidly", which is the adverb form of "intrepid". It means fearlessly, daringly, or resolutely.
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The noun forms for the verb to persist are persister, persistence, and the gerund, persisting.
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