A figure like Almachius appears in virtually every virgin martyr legend. He is the yin to the saint's yang. He's the dark, evil figure whose tyranny the saint must confront, usually in the form of the painful torture and death he decrees. Sure, he's evil, but he's also absolutely essential to the form of the martyr legend, because without him, the saint has no way to test and prove her holiness. Almachius plays his part well: not only does he decree a torturous death-by-cauldron-boiling and beheading for Cecilia, he also calls her before him for a verbal sparring match that allows Cecilia to prove her steadfastness of faith and her superior argumentative skills.
As a villain, Almachius's tragic flaw is overconfidence: to Cecilia he boasts that his princes have given him power "to maken folk to dyen or to lyven" (472). His claim that he has the power the power of life and death is extremely arrogant by any standard, but this boast is definitively proven wrong when Cecilia just plain refuses to die when he orders it. Almachius's arrogance is probably the reason that, unlike the other formerly evil characters in the tale, Cecilia is unable to convert him: he's just too hard-headed.
To Cecilia, moreover, Almachius's moral failings are evident in his argumentative errors: "Thou seydest no word, syn thou spak to me, / That I ne knew therwith thy nycetee, / And that thou were in every maner wise / A lewed officer and a veyn justise" (494-497). In the person of Almachius, then, the tale depicts a lack of rhetorical clarity as directly related to a lack of moral clarity.