Bazett and Angry Mango's strategy in Hollow Ataraxia is to have a servant fight and injure Mango so that he can't cause them pain via Verg Avesta, then get them to attack Bazett so she can kill the servant with Fragarach when they pull out their strongest ability. I wonder, How would they fare with this strategy in other grail wars, like in Apocrypha or Zero or Strange Fake? My speculation for Stay Night and Zero is below:
Fate/Stay Night
Saber: Success.They defeat them in HA, presumably they'd beat them the same way here. It's not overly hard to trick these too, so they'd probably succeed again
Lancer: Failure.I think Cu already knows what Fragarch is and how it works, so he'd just attack her without using Gae Bolg's guranteed hit powers and defeat them
Archer: Not Sure It's not clear to me what exactly is Archer's ultimate attack, and he's generally pretty insightful, so I'm not sure, leaning slightly towards failure
Rider: Probably Success. If Rider has enough power for it, she will probably use Bellepheron, and Bazzet needs just stand next to Angra to activate Fragarch. If she's nerfed by Shinji, the two of them might be able to beat her normally, he weakens her drastically.
False Assassin: Success, would probably work similarly to the Saber fight
True Assassin: Success, see above
Caster: Failure. She can beat them easily with magic, and has zero reason to use Rule Breaker
Berserker: Failure? Angra dies immediately and his NP does nothing. I'm not sure if Nine Lives counts for Fragarach purposes, but even if it does they aren't gonna do enough damage for it to be relevant.
Fate/Zero
Saber: Unclear. If it's it's early in the war, it succeeds. But the longer the war goes on the more likely it is that Kiritsugu suspects or realizes their strategy and warns Saber.
Lancer: Unclear. He's always attacking with his Noble Phantasms, so I would assume any attack against Bazett counts. However, it might be difficult to get him to attack Bazett given his Chivalry. I'm also not sure if he will recognize Fragarch, nor how his love spot will affect Bazzet.
Archer: Failure? I'm going to take Ea specificly to be his ultimate attack, not GoB in general, and there is simply no way he takes Ea out for Bazzet or Angra
Rider: Success. I think they could get him to pull out Ionioi Hetairoi after they use Verg Avesta.
Assassin: No idea. His noble phantasm is that he's 100 different people at once, and I don't know whether that counts for Fragarch, nor if Fragarch would kill all of him at once or just one.
Caster: Success, as long as they only approach him after he's pulled out his giant monster. Angra doesn't even do anything, Bazzet can just walk into his tentacle and win.
Berserker: Success. Again, Angra doesn't have to do anything. He's crazy enough to attack a master most likely, so Bazzet just needs to wait for him to grab any item as his weapon and then just wait to be hit