1) In manner unyielding 2) Inflexibly 3) Insistently 4) Unshakably 5) With conviction 6) With no sign of caving 7) With no sign of giving in 8) Without wavering Found on https://www.crosswordclues.com/clue/adamantly
[Adverb] Firmly, strongly. With a fixed idea which cannot be changed. Example: He is adamantly opposed to fox hunting.
Found on http://www.bbc.co.uk/skillswise/glossary/