While this question is fantasy-based, this answer is reality-based in that it doesn't require that the hero know about the AI at all until after the fight has started, if at all, and doesn't require any magic or unusual equipment.
As a martial artist (a red belt/4th kyu in Shotokan karate and hapkido), I have fought dan-grade black belts. The difference is not as great as many people seem to think, and is on the order of perhaps a tenth of a second and the sheer variety of things that they can do and counter. Attack a high-ranked martial artist, and it is likely that - precognition or not - they will have experienced that attack before and can defend against it. On the other hand, I have scored hits against my sensei, who is approaching the rank described in the question, however it is a matter of probability, and the probability is that for the most part, I'll be hit more often than I'll score a hit.
Also, I've fought dan-grade juniors (under 16) as a red-belt and below, and as an adult in my 40s, they aren't much of a threat - they can execute all the techniques better than I can, and they know more, but they can't string it all together for as long - they lose the plot after a few techniques, while I can keep planning and acting while they lose their concentration, so as long as I can hold off their initial attacks, I'm pretty sure I'll score. That's why there are age groups in tournaments.
Now, depending on the skill of the chronos cultist - which may not actually be nearly as high as Alice's as he would have been relying on precognition to deal with similar ranked or lower ranked opponents, thus actually reducing his chance for independent learning - it may not actually matter that the cultist has precognition.
The first likely option that I can see if Alice is indeed capable of defeating the cultist hand-to-hand is that the cultist runs away or surrenders immediately, having been told by the AI that he can't win, precognition or not.
The second option is that the fight will take longer than six seconds. One of the exercises we practice involves fighting six to ten other fighters one after the other, ten seconds for each other opponent. During those ten seconds, there may be a lot of hits scored, or none at all, however fighting non-stop for that time can get pretty exhausting. In a fight between high-dan martial artists (or those who can act as if they were), there may be quite some time of exchanging ineffective and only mildly effective blows before the telling blow is scored.
Unlike in tournament fighting, real fighting is not to the first touch. An opponent may score a hit that was mostly deflected. Also, there are rarely any breaks while the judges call out the scores. So, our two martial artists might be fighting for some time. In my dojo, black belt (0-dan) students must fight for ten minutes non-stop in grading. Can the Chronos cultist match that kind of endurance? It is unlikely, given that he'd probably win most fights in the first 6 seconds. He would probably have trained, but he would be training for strength, to get his blows out faster, rather than for the endurance to outlast an opponent, given that he'd be used to winning quickly, and any injuries he might take would be from faster opponents.
So, the fight between Alice and the cultist (assuming it happens at all) would go like this:
The pair square off and begin circling one-another. The AI tells the cultist that this fight won't be won quickly, but the highest order of probability to inflict impairing damage on Alice is to do X, Y, Z and so on, which the cultist dutifully does, immediately going on the offensive. Alice may or may not actually take any hits, but they'll probably be minor if she does at this stage, and she may score some similarly minor hits of her own. This rapid exchange of blows would continue for some time, potentially up to a minute, and all the while both fighters will be getting tired.
At some point, Alice may realise that the cultist is predicting her moves before she makes them, and from that point onward, she would fight more conservatively and defensively, always keeping her defensive options open, so while the cultist may be told the best sequence of actions, they won't necessarily be good enough against the better martial artist
However, Alice, having better training, would have longer endurance, and the gap between the cultist and Alice will gradually widen. Alice will begin scoring more and potentially better hits as exhaustion begins to slow the cultist more than it slows her.
As Alice observes the cultist slowing due to exhaustion, she can begin going back on the offensive. There is a difference between knowing what an opponent will do, and having the ability to counter that opponent, and despite attempting all the correct counters, the cultist will take more and more minor and less-than-minor hits.
Then, the AI will realise that in six seconds the fight will be over, with the cultist as the loser, and there is no way out of this situation, as the AI/Cultist lost almost a minute ago, as the cultist's level of exhaustion passed the point where victory or escape was impossible, however the ultimate conclusion took more than 6 seconds to foresee.
As the AI has foreseen, Alice delivers the final, telling sequence of attacks that fells the cultist.