WordNet sense 1 (marked by firm determination or resolution; not shakable):

firm, steadfast, steady, stiff, unfaltering, unwavering, unbendable

WordNet sense 2 (firm in purpose or belief; characterized by firmness and determination):

resolute

WordNet sense 3 (without flaws or loopholes):

bulletproof, unassailable, watertight

WordNet sense 4 (incapable of being contested or disputed):

incontestable, incontestible