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Synonyms for Unshakable (same or very similar meaning)

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):

WordNet sense 3 (without flaws or loopholes):
bulletproof, unassailable, watertight

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

From the ODE community, based on WordNetadd/edit