firm, steadfast, steady, stiff, unbendable, unfaltering, unshakable, unwavering -- (marked by firm determination or resolution; not shakable; "firm convictions"; "a firm mouth"; "steadfast resolve"; "a man of unbendable perseverence"; "unwavering loyalty")
unassailable, unshakable, watertight, bulletproof -- (without flaws or loopholes; "an ironclad contract"; "a watertight alibi"; "a bulletproof argument")